时间：2022-10-17 12:37:12
Abstract. Using actuarial techniques， the study estimates the fund gap of pooling account and individual account respectively on on enterprise worker’s basic endowment insurance in Hebei province. And based on the estimation， the study puts forward four policy suggestions： expand the coverage of the pension scheme； revised the number of months of the annuities； increase the level of interest； improve financial support.
Key words： endowment insurance； actuary； pooling account； individual account； gap
1. Introduction
The problem of the endowment insurance fund gap formed in the process of the transition of the basic endowment insurance in China from the pay-as-you-go system to "combination of the social pooling and the individual account" has always been the problem the central and the local governments as well as the theory circle are well concerned about. In December， 2011， "China pension development report 2011" edited by the well-known social security expert Mr. Zheng Bingwen was officially released at the International Forum on social security in China Academy of Social Sciences （2011）. The report points out that the China pension system is facing severe challenges. On the one hand， in nearly half of the province， the pension income has more expenditures than the income， and on the other hand， the income balance rate of the fund is significantly lower than the rate of the inflation. According to the statistics of the Ministry of human resources and social security in 2010， excluding the financial subsidy of 195.4 billion Yuan， there is a total of 15 provinces （including the Xinjiang Construction Corps） whose paid income of the current period of the basic old-age insurance in the corporate sector is over the expenditure， with the gap up to 67.9 billion Yuan. This means that the financial risks of the potential Chinese pension system have the dominant trend， even to the extent that is hard to leave the fiscal subsidies. Dealing with the funding gap， should we start from within the systems， to improve the payment level or delay the retirement age？ Or starting from outside the system， should we expand the participation scope of the basic old-age insurance， or whether should the pension fund be in the stock market？ Can the market solve the problem？ This paper will be based on the estimate of the fund gap of the endowment insurance in Hebei province using the actuarial technology， to answer these questions above， and give the policies and recommendations.
2. Research overview
In terms of the researches on the fund gap of the basic endowment insurance， in the theory circle， there are three main research directions. The first is to start from the causes of the funding gap， to study the countermeasures. Mei Qiong and Chi Wentie （2010） analyze from the causes of the formation of the pension gap， and conclude that the gap of the pension in China comes from the fund gap of the personal account and the social pooling account， and put forward the suggestion to narrow the gap according to the different reasons. The second is the establishment of the fund gap model， and have the quantitative analysis， so as to put forward some countermeasures from the angle of the actuarial techniques. Gao Jianwei and Ding Kequan （2006） set up an actuarial model of the fund gap of China's basic old-age insurance using the actuarial techniques. And using the model， they have the analysis of the risk ranking and the sensitivity of the factors affecting the fund gap of the basic endowment insurance， and conclude that the main factors influencing the fund gap of the pension insurance， in order to give reasonable suggestions to reduce the funding gap. The third is that the validity of these solutions is analyzed. Sun Bo， Dong Keyong and Tang Yuanzhi （2011） simulate the development trend of the urban population from 2010 to 2080 under the adjustment schemes of different family planning policies， and estimates the development trends and the difference of the gap of the urban basic pension. This article will use the actuarial techniques to establish the fund gap model of the basic old-age insurance in Hebei Province， estimate the fund gap of the basic endowment insurance between 2012 and 2080， and focus on the analysis whether the pension insurance fund entering the market is able to resolve the gap.
3. Build the model
The basic old-age insurance in our country at present include the basic old-age insurance for the urban workers， the basic old-age insurance for the urban residents and the new type of rural social endowment insurance. But because the basic old-age insurance for urban residents and the new rural social pension insurance had taken the "combination of the social pooling and the individual account" old-age insurance system at the beginning of the implementation， the fund gap of the old-age insurance in our country is the cost of the system generated in the process of the transition of the basic old-age insurance for the urban workers from the "institutional pay-as-you-go" to the "combination of the social pooling and the individual account". Therefore， in this paper， the gap analysis of the basic old-age insurance funds only considers the basic old-age insurance for urban workers.
In accordance with the relevant regulations， the basic old-age insurance for the urban workers is divided into two parts of the pooling account and the individual account. At present， a lot of researches will be combining the pooling account and the individual accounts together to consider the fund gap， thus obscuring the real problem of the individual account. Therefore， this paper will consider the account fund gap and the personal account fund gap respectively.
3-1. The calculation model of the fund gap in the pooling account
The pooling account income includes the basic old-age insurance paid in accordance with the 20% of the total wages of all the enterprise staff in the last month. The enterprises whose base payments are below 60% of the average wages of the staff and the workers and the total wages cannot be approved can pay the basic endowment insurance according to the base payment of the employees.
The spending of the pooling account includes the personal pension accounts paid from the forehead its individual account stores of the retired workers. Those with insufficient individual account stores or without the basic pension will be paid from the social pool fund. The fundamental annuities， the transitional pension and the subsidies will be paid by the social pooling fund. The basic pension increased by the normal adjustment of the mechanisms， according to the proportion of the basic old-age pension in the personal accounts for the employee retirement pensions， will be paid respectively from the individual account balance and the social pooling fund column.
Because the next part of the amount of the personal account is explained in detail in the calculation model for the fund gap of the personal accounts， therefore， in order for the simple analysis， consider only the expenditure of the basic pension. According to the basic endowment insurance paying method of the enterprise workers in Hebei province （Office word [2006] 77）， the basic pension = （the average monthly salary of the on-the-job staff and workers of the province in the last year when the insured staff is retired + the index average monthly payment of the individual wages） ÷ 2 × the fixed number of years of the capture expends （including the years as the payment， the same below） × 1%. Among them， the index average monthly wage of the individuals = the average monthly salary of the on-the-job staff and workers of the province in the last year when the insured staff is retired × average monthly wage index of the individuals.
The funds gap of the pooling account = the income of the pooling account the expenditure of the pooling account.
For simplicity， we assume in t years， the spending of all the pooling account = the number of the retired employees of the insured staff in the t years ×the average monthly salary of the on-the-job staff and workers of the province in the last year when the insured staff is retired × the fixed number of the years of the capture expends of the insured staff × 1%.
Namely，
In addition， this paper assumes that the income of all the pooling account in the t years = the total wages of the workers in the t years × 20% × （the number of insurance in the t years / the urban population）
Namely，
Then， the fund gap of the pooling account in the t years
Taking the year 2010 as an example， according to the Hebei Economic Yearbook in 2010， the insured workers in this year lt-lt ， r = 728.94 million people， and the retirees amounted to lt ， r= 259.5 million； 283.83 million Yuan. In accordance with the provisions of the average years of payment， those whose payment period is more than 15 years can receive the basic pension insurance. Assuming the person participates in the insurance at the age of 20， when he is retired at the age of 60， the longest fixed number of years of the capture expends is 40 years. Taking into account the process of the reform of the basic endowment insurance in China， we assume that in 2010， the average fixed number of years of the capture expends is 20 years， and after that， the annual rise is 1 year， until 2030， it will reach 40 years.
Then，
=10249.67 million Yuan.
According to the Hebei Economic Yearbook， the annual growth rate of the average wages of the workers in the 20 years from 1990 to 2009 is 14%， and the average growth rate of the total wages over the same period is 12%. We assume that the growth rate of the average wages of the workers in the next 20 years remains 14%， and the total wages of the staff and workers will sustain a growth rate of 12%.
In terms of the predictions for the injured workers， according to the average annual growth rate of 0.53% of the total population of Hebei province from 2000 to 2009， the linear growth of the proportion of the urban population will reach 60% in 2030 （the level of the international cities）， and the number of workers accounted for the proportion of the urban population will increase by 1 per cent per year. The number of retirees will cover 0.2 of the percentage points of the percentage of the annual growth of workers， from which we can obtain the predicted value of the paying workers and the retired employees from 2011 to 2030.
Into the formula， we can get the fund revenue and the expenditure gap each year from 2010 to 2030.
According to the 5% of the discount rate， from 2010 to 2030， the value of the fund gap will reach up to 23.7 thousand billion Yuan. There are three effective ways to reduce the pooling fund gap. The first is to broaden the scope of the insurance participation， namely improve the value of . The second is to improve the rate of the payment， that is， increase the 20% to more than 20%. The third is to reduce the pension replacement rate， that is， to reduce the 1% to less than 1%. According to the present situation of the Chinese social security levels， the latter two kinds of measures are not realistic， and are easy to form new social problems， so the best way is to broaden the scope of the insurance participation.
3-2. The funding gap of the personal account
According to the basic endowment insurance paying method of the enterprise workers in Hebei province （Office word [2006] 77）， the monthly retirement pension in the personal pension accounts = the accumulated amount of individual account ÷ the corresponding paying months of the retirement age of the individuals. The amount of the payment in the personal account is the primary endowment insurance paid by eight percent of the actual wages of the individual workers in the last month， and all will enter into the personal account. If the individual base payment is less than 60% of the average monthly salary of the on-the-job， workers of that year， pay the fees according to 60% of the province's average monthly wage of the employees. And if it is higher than 300% of the average monthly salary of the on-the-job， workers in the province of that year， pay the fees according to 300% of the province's average monthly wage of the employees. Luo Zhengqing and Lu An （2010） according to the state-issued [2005] 38 paper， step up the actuarial model for the fund gap of the personal account. In references to the research results， note the present value of the gap in the retirement year of the receivers is Q， then
is the actuarial present value of the life annuity of x years after the deferred n years to pay 12 times for the years. Note the paying months are N， and the retirement age is X， and the accumulated amount of individual account in the retirement years is Gx.
According to the current one-year time deposit rate of 3.5% to calculate， the critical value of N is 349.323. Compared with the current paying months， no matter what age the retirement is， there is additional revenue， and no matter what age is for the retirement， there is the funding gap in the personal accounts.
According to the pension business （CL4） of the experience life table of the China life insurance industry （2000 - 2003）， while x=40， i=3.5%， Q=0.1682G
With the application of Excel， when the retirement ages range from 40 to 70 years old， and the rates i are respectively 3.5% and 5%， calculate the values of the fund gap Q/G in the personal account， and we can obtain the table.
From Figure 1 we can see that the fund gap in the personal account increases with the increasing of the retirement age， but it is also on the decline with the sensitivity of the increase of the retirement age in the discount rate I of the funding gap.
Luo Zhengqing and Lu An （2010） think that the factors that influence the fund gap of the personal account are： （1） the inheritance； （2） the paying months； （3） the interest rate. But the author thinks that， firstly， the inheritance is not the factor affecting the fund gap of the personal account， because the business annuity can also inherit the balance of categories of the products. As long as we take the inheritance into account when we design the system， to determine the contribution rate， the monthly paying amount and other factors， the gap can be avoided. Secondly， in terms of the monthly paying amount， when we design the systems， assume ， then the fund gap can also be zero. Thirdly， from the above table and the figure， as can be seen， with the rise of the interest rates， the fund gap decreases obviously. But with the rise of the retirement age， the decline of the funding gap also decreases.
4. Conclusions and policy recommendations
Based on the analysis of the fund gap of the pooling account and the fund gap of the personal account in the basic endowment insurance of the enterprise workers in Hebei province， the author of this paper puts forward the following three aspects of policy recommendations to reduce the funding gap in the basic endowment insurance of the company workers：
4-1. Make efforts to broaden the scope of the insurance participation.
The pooling account has the property of pay-as-you-go system， and the broadening of the scope will increase the income of the pooling account fees， which is an effective measure to offset the expenditure of the pooling funds.
4-2. Scientifically determine the paying months.
Make full use of the actuarial techniques to determine the paying months， to reduce the fund gap of the personal account. Or make use of the defined contribution pension （DC） technology， and determine the expenditure based on the income according to the income level of the individual account.
4-3. Raise the levels of the interest rates.
Broaden the investment channels， and improve the investment interest of the basic old-age insurance， which is favorable to the reduction of the fund gap of the personal account. For example， in accordance with the American 401k plan， after the permission of the insured individuals， a certain proportion of personal account funds can be invested in the stock market. The rate of return on investment of the national social security funds over the past ten years also confirms that expanding the investment channels can increase the rate of the return.
In addition to the above three kinds of technological measures， in order to effectively cope with the huge gap in the pooling funds over the next few decades， the finance must increase the investment， increase the proportion of the social security spending in the fiscal expenditures， and prevent the fund gap accumulated to a certain degree from affecting the realization of the individual account， and even forming the situation that the finance cannot afford.
References
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