^{1}- Assistant Professor, ECO College of Insurance, . . tehran.iran.AllamehTabataba'i University

^{2}- ECO College of Insurance, AllamehTabataba'i . tehran.iran. University

چکیده

Abstract
Employees always concern about losing their job, or in other word, losing their income resources. For this purpose, governments require strong protection system for covering these concerns. The Unemployment Insurance (UI) program’s can be used for achieving this goal.
Based on article five of Iranian unemployment Insurance law, premium is four percent of employee’s salary while employer and government’s contribution is four percent and one percent, respectively. Hence, there are great concerns about the financial pressure on the government regarding implementing this law.
In this paper, we price UI based on the insurance history of employee and the duration of being unemployed. We use the Weibull distribution for finding duration of unemployment, and finally equivalence principle applied for finding the fair UI premium rate. Our findings indicate that the UI rate is less than 4% which is lower than current UI rate in Iran which has been set by law. Consequently, government’s contribution can be eliminated which reduces concerns about providing required budget by the government.

Employees always concern about losing their job, or in other word, losing their income resources. For this purpose, governments require strong protection system for covering these concerns. The Unemployment Insurance (UI) program’s can be used for achieving this goal.

Based on article five of Iranian unemployment Insurance law, premium is four percent of employee’s salary while employer and government’s contribution is four percent and one percent, respectively. Hence, there are great concerns about the financial pressure on the government regarding implementing this law.

In this paper, we price UI based on the insurance history of employee and the duration of being unemployed. We use the Weibull distribution for finding duration of unemployment, and finally equivalence principle applied for finding the fair UI premium rate. Our findings indicate that the UI rate is less than 4% which is lower than current UI rate in Iran which has been set by law. Consequently, government’s contribution can be eliminated which reduces concerns about providing required budget by the government.

The unemployment insurance is one of the most important services which can be provided for employed people since there is always a probability of losing their job. For protecting and supporting people who being unemployed or who that looking for job, every government needs to have some appropriate programs to repel this problem. Hence, unemployment compensation is a social program designed to replace part of lost earnings for people with prior work experience. Unemployment Insurance (UI) programs vary quite a bit because of country- or region-specific concerns. UI provides benefits to persons who are unemployed through no fault of their own and who are ready, willing and able to work, and actively seeking work.

Since unemployment insurance was created in 1935, it has expanded into a broad, employer-based program that aims to help to stabilize the overall economy and protect the unemployed from major financial disruptions. There are four major types of unemployment compensation programs around the world, namely, compulsory unemployment insurance, voluntary unemployment insurance, unemployment subsidy, and firing fee. The compulsory unemployment insurance is the most commonly-used program worldwide. In most countries unemployment insurance (UI) is nationalized and people who work are required to pay a compulsory insurance premium (contribution). In fact, most unemployment insurance schemes charge a flat percentage of a worker’s income earned between some minimum and maximum levels.

In Iran, people who are subject to the Social Security Law shall be entitled to the rules and regulations of the present Law. Retired and totally disabled, self employed and the voluntary insured and foreigners residing in Iran are excluded from entitlement to the law. According to the Law, an unemployed person shall be defined as an insured person ready for work, made unemployed due to reasons other than his or her own fault.

Based on article five of Iranian unemployment Insurance law, premium (which will be called contribution rate from this point forward) is four percent of employee’s salary and must be paid by his employer and the government. Employer and government’s contribution is three percent and one percent, respectively.

There have been great concerns about the financial pressure on the government regarding implementing this law. In response to the above mentioned concerns, in this research we are going to calculate the fair contribution rate. If results show that the optimal contribution rate is less than or equal to three percent, then government’s contribution can be eliminated which reduces the financial pressure of implementing the law.

The main question of this research: what is the optimal contribution rate?

In order to answer the main question of the research, we construct the below hypothesis:

The optimal UI rate, which is calculated in this paper, is less than the current 4% UI rate in Iran which is set by law.

This paper is organized as follow:

In section 2, we present a review of the literature in deriving actuarially fair unemployment insurance contribution rate, the level and length of unemployment insurance benefits, job search theory, and effect of unemployment duration.

In section 3, we describe the equivalence principle, CAPM based model, and modeling unemployment duration with respect to Weibull distribution.

Finding the unemployment duration, and deriving the actuarially fair premium with respect to the unemployment duration and the risk return of the market and insurance company with empirical data will presented in chapter 4.

The conclusion and suggestions are provided in Chapter 5.

Literature Review

The original contribution of the search theory was the theoretic approach to the analysis of unemployment spells durations and dispersion of incomes. Theory of job search uses the tools of sequential statistical decision theory for the typical worker’s problem of finding a job in a decentralized labor market.

Bronars (1985) derived actuarially fair unemployment insurance premiums in a theoretical model of a regulated private market for unemployment insurance. Fair premiums are derived using the capital asset pricing model under the assumption that insurance firms borrow and lend in the capital market to finance benefit payments. After that, Bronars obtained the empirical estimates of betas and fair premiums for the U.S unemployment insurance.

Meyer(Meyer 1990) tests the effects of the level and length of unemployment insurance benefits on unemployment durations. The paper tests the effects of the level and length of UI benefits on unemployment durations. Higher UI benefits are found to have a strong negative effect on the probability of leaving unemployment. However, the probability of leaving unemployment rises dramatically just prior to when benefits lapse. When the length of benefits is extended, the probability of a spell ending is high in the week benefits were previously expected to lapse.

Launov and etc(Launov 2004)investigate whether the extension of the entitlement to unemployment benefits in the mid 80s can explain the increase in the unemployment rates of unskilled and elder workers in western Germany. They found that for unskilled workers the extension of the entitlement period has significantly contributed to the changes in their search behavior. Unemployment rate for the unskilled predicted by the model shifts from 10.3% to 15.1% which almost completely matches the 9.2 % to 16.4 % increase of the same rate observed in the data.

Mehmet (TAŞÇI 2005) examines the determinants of unemployment duration for the first-time jobseekers in Turkey. He uses raw data from the Household Labor Force Surveys of 2000 and2001. He uses the grouped duration approach and finds that first-time jobseeker females are less likely to find a job compared to males. Urban resident males are more likely to find a job compared to rural resident ones. Increases in education level do not seem to decrease the hazard for both males and females.

Krueger(Mueller 2008) studied at Job Search and Unemployment Insurance. This paper provides new evidence on job search intensity of the unemployed in the U.S., modeling job search intensity as time allocated to job search activities. He finds that across the 50 states and D.C., job search is inversely related to the generosity of unemployment benefits. In addition, job search intensity for those eligible for UI increases prior to benefit exhaustion.

Hwei-Lin Chuang and Min-Teh Yu (2010) studied at pricing unemployment insurance in case of Taiwan. This study incorporates the survival analysis of unemployment duration into the insurance pricing framework to measure the fairly-priced premium rate for Taiwan. Their results suggest that the fair premiums range from 0.2041% to 0.2436% under the 1999-2002 scheme and from 0.1388% to 0.1521% under the 2003-2009 scheme for various possible levels of average unemployment duration in Taiwan, and they are all lower than the current UI premium rate,1%.

Biagini and Widenmann ( 2012) worked at Pricing of unemployment insurance products with doubly stochastic Markov chains. They provide a new approach for modeling and calculating premiums for unemployment insurance products. The innovative modeling concept consists of combining the benchmark approach with its real-world pricing formula and Markov chain techniques in a doubly stochastic setting. They described individual insurance claims based on a special type of unemployment insurance contracts, which are offered on the private insurance market. The pricing formulas are first given in a general setting and then specified under the assumption that the individual employment-unemployment process of an employee follows a time-homogeneous doubly stochastic Markov chain. In this framework, formulas for the premiums are provided depending on the Pnuméraire portfolio of the Benchmark approach. Under a simple assumption on the P-numéraire portfolio, the model is tested on its sensitivities to several parameters. With the same specification the model’s employment and unemployment intensities are estimated on public data of the Federal Employment Office in Germany.

Theoretical Foundation

In order to calculate the UI rate, we use different financial and statistical models. In this part we provide explanations about the models that we have used in this paper.

CAPM Model

We consider CAPM (Capital Asset Pricing Model) –based insurance pricing model. Specification of the Weibull distribution is used to estimate the unemployment duration. We then set up our formulae to determine the actuarially fair contribution rate for the UI program.

The fairly-priced insurance contribution requires that the present value of premium income (PV(I)) equals the present value of loss payments (PV(L)). This corresponds to the equivalence principle. Fairley (1979) introduced this pricing approach in the property-liability insurance literature for the first time. He applied the CAPM to derive risk-adjusted rates of return for property-liability insurers.

Important extensions of the Fairley model by Myers and Cohn (Myers 1981) and Hill and Modigliani (Hill 1987) provides empirical evidence on its reliability and stability. Bronars (1985), Beenstock and Brassee (1986), and Blake and Beesnstock (1988) have applied the CAPM-based framework to study unemployment insurance with different focuses.

We can express the present value of the expected contribution rate (I) and expected loss (L) as follow:

PV(I)=PV(L) (1)

(2)

(3)

Where n=0,1,…,N , I_{n} denotes the expected contributions received at time n , L_{n} denotes the expected losses paid at time n , R_{f} denotes the risk-free rate of interest , and R_{L }denotes the risk-adjusted return from CAPM for whole insurance field in all insurance company. That is, R_{L }has the following relationship with the market

Portfolio returns, R_{m}.

E(R_{L}) - R_{f}= β (E(R_{m}) - R_{f}) (4)

Weibull distribution

We apply Weibull distribution in Unemployment Duration. The probability density function of Weibull distribution is

The instantaneous hazard rate is , an increasing, constatnt, or decreasing function of t as p is greater than, equal to, or less than unity. This property is interesting when the Weibull distribution is used as a waiting time distribution because it determines whether the probability of an event occurring in the period between t and t+Δt is an increasing, constant, or decreasing function of the elapsed time t.^{[i]}

One of the reasons for the widespread use of the Weibull has been its capacity for dealing with duration dependence: the extent to which the conditional hazard of the event of interest occurring is increasing or decreasing over time. Weibull model allows the extent of duration dependence to vary according to a specified set of covariates. For this reason, it is an appropriate distribution for unemployment duration.

In calculating the benefit payment we need to estimate the average duration for the claims paid. As unemployment duration has the problem of incomplete spells, it is inappropriate to use the statistical average of the unemployment duration in calculating the benefit payment.

To estimate the completed unemployment duration, a survival analysis derived from the job search theory should be applied. We will describe the procedure for calculating the benefit payment as follows.

Let T denote unemployment duration,T∈(0,∞) , and f (t) is the probability density function of T. The probability that the unemployment duration is less than t can then be expressed as:

(5)

Where F(t) denotes the cumulative density function of T. For an individual who has been unemployed for t periods, the conditional probability that he will leave the unemployed status (either transit to the employed or out-of-labor-force status) at time t is defined to be the hazard function (h(t)) and can be written as:

H(t) dt = Pr(t<T≤t+dt\T>t) = f(t)/S(t) (6)

where S(t) is the survival function defined to be:

(7)

As the Weibull distribution is most commonly used to describe unemployment duration in the literature (see Lancaster 1979, Lynch 1985, (Moffitt 1985), (Atkinson and Micklewright 1991), Hunt 1995, and Chuang 1999), we assume that the unemployment duration here follows the Weibull distribution in calculating the benefit payment of the UI program.

The hazard function and the survival function corresponding to the Weibull distribution are:

S(t) = exp(-(𝛌t)^{p}) (8)

h(t) = f(t)/S(t) = 𝛌p(𝛌t)^{p-1 } (9)

where p is the shape parameter, which determines the shape of the distribution, and λ is the scale parameter, which measures the time unit. The probability density function for the Weibull distribution can be derived from the survival function and the expected value of the unemployment duration can then be given as:

(10)

(11)

The expected value of the Weibull distribution can be written as:

(12)

Also the variance can be written as:

(13)

We use E(t) and Var(t) for calculating the scale parameter , and the shape parameter (p) .

Application to Iran’s UI scheme

Table 1 state the duration of unemployment benefit in Iran with respect to the insurance history and marital status.

According to the rules implemented in the UI program in Iran, the benefit payment amount is 70% for the first 6 months, 60% for the second 6 months, and 50% for the third 6 months of the claimant’s insured earnings. For married insured, this amount increases by 10% of earning for each period.

Table 1 Iran’s UI scheme.

Insurance history

(months)

Maximum benefit duration with respect to the marital status (months)

Married

Single

12 to 24 months

9

6

25 to 60 months

12

9

61 to 90 months

15

12

91 to 120 months

18

15

121 to 150 months

21

18

151 to 180 months

24

21

181 to 210 months

28

24

211 to 252 months

32

27

More than 253 months

36

30

Duration of benefit payment

Based on the above information, we can derive the expected duration of the benefit payments for a representative claimant as:

For single person:

where D denotes the expected duration of benefit payment.

is the probability that the individual has 12 to 24 months of insurance history, is the probability that the individual has 25 to 60 months of insurance history, is the probability that the individual has 61 to 90 months of insurance history, is the probability that the individual has 91 to 120 months of insurance history, is the probability that the individual has 121 to 150 months of insurance history, is the probability that the individual has 151 to 180 months of insurance history, is the probability that the individual has 181 to 210 months of insurance history, is the probability that the individual has 211 to 252 months of insurance history, and is the probability that the individual has an insurance history of more than 253 months.

For a married person we have:

(15)

Fairly-Priced Premium Rate (Y)

Combining the CAPM-based insurance pricing framework and the weibull specification, we express the present value of the expected benefit payment ( ) as the following:

(16)

Where and are the monthly returns and denotes the expected benefit payment to a representative individual. Term W denotes the insured monthly earnings and U is the unemployment probability.

Assuming a representative individual works and pays the premium for 30 years in his/her lifetime, then the present value of the expected premium income ( ) received from the representative individual is expressed as:

(17)

Where Y denotes the premium rate.

The fairly-priced UI premium can be derived by solving Y from equating and .

The Measurement of parameters

Based on equations (14) to (17), we have grouped the parameters in our model into three types. The first type is related to the unemployment situation, such as the parameters (pand λ) of the Weibull distribution and the unemployment probability. The second type describes the insurance characteristics of the UI program, such as the proportions of insured workers with various years of insurance history. The third type includes variables and parameters of the capital markets, such as the systematic risk coefficient (β), risk-free rate of interest, and the rate of return of market portfolio.

The sources and measurements of parameters used in our model are reported in table 2. The parameter values of the Weibull distribution were calculated by solving the mean and variance formulae simultaneously based on the estimated values of means in recent literature and variance from simulated data.

Table 2 Sources of Parameter and Measurement

Parameters

Measurement

Data Sources

Shape parameter (p) of Weibull distribution

Solved from mean and variance

formulae of Weibull distribution.

Mean values are taken from

recent literatures and variance is

computed from simulated data.

Scale parameter (λ) of Weibull distribution

Solved from mean and variance

formulae of Weibull distribution.

Mean values are taken from

recent literatures and variance is

computed from simulated data.

Unemployment probability (U)

Proportion of previously employed workers who become unemployed in the current years.

Reported with Census Center (Statistical Center of Iran).

Proportion of insured workers with 12 to 24 months insurance history(α_{1})

Proportion of person with 10 to 24 years old in Economically active population.

Reported with Census Center (Statistical Center of Iran) in Iran Statistical Year Book.

Proportion of insured workers with 25 to 60 months insurance history (α_{2})

Proportion of person with 25 to 29 years old in Economically active population.

Reported with Census Center (Statistical Center of Iran) in Iran Statistical Year Book.

Proportion of insured workers with 61 to 90 months insurance history(α_{3})

Proportion of person with 30 to 34 years old in Economically active population.

Reported with Census Center (Statistical Center of Iran) in Iran Statistical Year Book.

Proportion of insured workers with 91 to 120 months insurance history(α_{4})

Proportion of person with 35 to 39 years old in Economically active population.

Reported with Census Center (Statistical Center of Iran) in Iran Statistical Year Book.

Proportion of insured workers with 121 to 150 months insurance history(α_{5})

Proportion of person with 40 to 44 years old in Economically active population.

Reported with Census Center (Statistical Center of Iran) in Iran Statistical Year Book.

Proportion of insured workers with 151 to 180 months insurance history(α_{6})

Proportion of person with 45 to 49 years old in Economically active population.

Reported with Census Center (Statistical Center of Iran) in Iran Statistical Year Book.

Proportion of insured workers with 181 to 210 months insurance history(α_{7})

Proportion of person with 50 to 54 years old in Economically active population.

Reported with Census Center (Statistical Center of Iran) in Iran Statistical Year Book.

Proportion of insured workers with 211 to 252 months insurance history(α_{8})

Proportion of person with 55 to 59 years old in Economically active population.

Reported with Census Center (Statistical Center of Iran) in Iran Statistical Year Book.

2.Estimated using daily data from Tehran Stock Exchange.

Assumption

Because of lack of data, we have made some assumptions. We present these assumptions as below:

A person

1- With 10 to 24 years old has 12 to 24 months insurance history. So can be calculated by this assumption.

2- With 25 to 29 years old has 25 to 60 months insurance history. So can be calculated by this assumption.

3- With 30 to 34 years old has 61 to 90 months insurance history. So can be calculated by this assumption.

4- With 35 to 39 years old has 91 to 120 months insurance history. So can be calculated by this assumption.

5- With 40 to 44 years old has 121 to 150 months insurance history. So can be calculated by this assumption.

6- With 45 to 49 years old has 151 to 180 months insurance history. So can be calculated by this assumption.

7- With 50 to 54 years old has 181 to 210 months insurance history. So can be calculated by this assumption.

8- With 55 to 59 years old has 211 to 252 months insurance history. So can be calculated by this assumption.

9- With 60 and more years old has 253 and more months insurance history.

Numerical Illustration

In this section, we apply the methods that have been discussed to the real data.First we calculate the β of Insurance industry with respect to the Market from CAPM with real data. In the next steps, we find unemployment duration (D) by considering Weibull distribution. Then we use the results for calculating the UI rate (Y). Finally, we show the effect of changing the value of some parameters in Y.

Finding β of Insurance Industry

We have two amounts for β.

β which is stated in Sepahan Bank report that equals 13%.

β that we calculate in following section. Hence we need below data:

R_{L} :Risk-adjusted return for whole insurance field in all insurance company.

Source: Tehran Stock Exchange.

R_{m} :Market-portfolio returns. Source: Tehran Stock Exchange.

R_{f}:Risk-free rate of interest. R_{f}= 15% reported by Central Insurance of IR Iran.

From CAPM model that introduced in chapter 3, we have following equation (equation 4 in chapter 3):

E(R_{L}) - R_{f}= β (E(R_{m}) - R_{f})

For calculating β, we regress the R_{L} on R_{m} .

The result show that the β is equals 27%.

Consequently, for calculating the UI rate, we consider two scenarios, the first one related to β=13% and the second one related to β=27%.

Duration of Benefit Payment ( D )

Finding the parameters of Weibull distribution

For calculating these parameters, it’s necessary to have a mean and variance of unemployment duration or the duration of finding job for an unemployed person.

Salehi-Isfahani and Egel (2010)^{[iii]} found that the mean duration of joblessness for men and women is 15 and 37.5 months, respectively.

For finding the variance of unemployment duration, we have to simulate the value in this range. For this reason, we consider total economically active population in Iran which is 23,469,000 persons^{[iv]}. The total men in economically active population are 19,840,000 persons (84% of whole active population) and the total women are 3,629,000 persons (16% of whole active population). So the mean duration of unemployment calculate as follow:

Mean duration of unemployment = (0.84 * 15) + (0.16 * 37.5) = 18.6 months

The simulated variance is equals to 166 months.

Let mean and variance in (12) and (13) in chapter 3.

By solving this two equation, the shape parameter( p) and the scale parameter ( λ ) of Weibull distribution find as follow:

p= 8.01 , λ= 0.0018

Calculating the duration of benefit payment ( D )

As we have seen in chapter 3, according to the unemployment scheme in Iran, we have we can divide people based on their marital status. However, we only consider married people. Although maximum duration of benefit payment for married people is greater than the single people, however, both groups pay the same contribution rate. In fact, we consider the worst scenario for calculating D (maximum value for D). then we can compare the rate for the worst scenario with the current rate which is set by law.

The parameters and their value for this purpose calculate as follow:

This amount shows that the duration of benefit payment is 393 days , in other words, the duration of benefit payment (D) for married persons is about 13 months.

Calculating the Fairly-Priced contribution rate (Y)

As we expressed in chapter 3, we apply equivalence principle for finding the fair premium. So we have to find the present value of the expected benefit payment ( ) and the present value of the expected premium income ( ) of insurance company.

Calculating the present value of the expected benefit payment ( )

As equation (16) expressed, we need the monthly returns.

Note : Suppose the annual interest rate is i . For calculating m-thly payment of interest rate, we have

1+i=(1+i^{(m)}/m)^{m}

So we have

1+R_{f}=(1+R_{f}^{’})^{12}

Where R_{f}^{’} is monthly risk free rate.

Let R_{f} = 0.15 , so we can write last equation as

1+0.15=(1+R_{f}^{’})^{12}

R_{f}^{’}=0.011

Now we are going to calculate the probability of losing the job for a persons in a specific years. For this purpose we consider the number of people who lose their job in a year and divided this value by total workers in the begining of the year.

From the report of Social Security Organization of Iran, we calculate this amount:

Total number of employed people reported 20,476,000 persons. And the report shows that 409,525 people losses his/her job.

So we have

U=(Total people who losses his/her job)/(whole employed people)

U=409,525/20,476,000=0.02

This value show that with probability of 2% , it’s possible for each person that loss his/her job.

The value of 0.8 in the equation denote the benefit payment amount of the claimant’s insured arnings.

As we previously explained, this amount is 70% for first 6 months, 60% for second 6 months and 50% for third 6 months for the case of single insured. And for married insured, this amount is 80% for first 6 months, 70% for second 6 months and 60% for third 6 months.

- Why we apply 80% for this amount?

- Since this value is greater than the other, for single and for married case, we consider the worst case for our calculating and the measure of Y based on this amount is the maximum Y that can be calculate.

By considering this amount for benefit payment and the maximum duration of benefit payment, the value of Y that we are going to calculate is the maximum amount for Y, and in any other case for insured status and period of benefit payment, the amount of Y is more less than this amount of Y.

In final step, we consider two value of β . The first β is 13% which state in Sepahan Bank, and the other is 27% that we calculate in 4-3-2 from CAPM model.

Now we calculate Y based on two values of β.

By equating (16) and (17), we derive the fairly-priced UI premium (Y).

The parameters and their measure that we need:

D=13, U=0.02, R_{f} = 0.15

R’_{f} = 0.011, E(R’_{m}) = 0.022

1- The case of β =0.13 :

Y = 0.0268

In other word the UI premium rate is 2.68%.

2- The case of β =0.27 :

Y = 0.0266

In other word the UI premium rate is 2.66%.

As we see in this part, we find that the fair premium rate is less than the current premium rate in Iran which is 4%.

By knowing this fact that this 2.68% or 2.66% is maximum premium rate and it’s probable that the fair premium rate be more less than this value.

Changing the value of Parameters

In this section we are going to show the effect of changing some parameters on the premium rate.

Table 4

Fair Premiums (Y) under Alternative Values of the Shape Parameter (p) of

Unemployment Duration Distribution

β =0.13

Table 5- Fair Premiums (Y) under Alternative Values of Hazard Rate Parameter (λ)

P

D ( Months)

Y (%)

5

12.51

2.496

5.5

12.62

2.5

6

12.7

2.521

6.5

12.81

2.5433

7

12.9

2.591

7.5

12.97

2.6412

8.01

13

2.68

8.5

13.6

2.6881

9

13.73

2.6899

9.5

13.81

2.6954

10

13.94

2.6981

10.5

13.99

2.6999

11

14.5

2.87

- The fair premiums for the base case are in bold face.

The estimated unemployment duration (d) and fair premiums both increase with p .

β =0.13

λ

D ( Months)

Y (%)

0.0006

16.1

3.24

0.0008

15.8

3.068

0.0010

15.5

3.066

0.0012

15.1

3.065

0.0014

14.7

2.878

0.0016

14

2.877

0.0018

13

2.68

0.0020

12.6

2.496

0.0022

11.9

2.31

0.0024

11.3

2.30

0.0026

10.7

2.11

0.0028

10.1

2.10

0.0030

9.6

1.90

- The fair premiums for the base case are in bold face.

A higher value of hazard rate indicates that the unemployed are more likely totransit into employment. Thehazard rate should therefore be negatively related to the estimated unemployment /payment duration (d)and fair premiums(Y). Alternative values of λ have different effect on the values of fair premiums.

Table 6- Fair Premiums (Y) under Alternative Values of Unemployment Probability(U)

β =0.13

U

Y (%)

0.008

1.07

0.01

1.34

0.012

1.61

0.014

1.88

0.016

2.15

0.018

2.41

0.02

2.68

0.022

2.95

0.024

3.22

0.026

3.49

0.028

3.76

0.03

4

0.032

4.3

- The fair premiums for the base case are in bold face.

A higher value of unemployment probability leads to more unemployed workers, higher expected benefit payments, and higher fair premiums. The unemployment probability should therefore be positively related to the fair premiums (Y) .

Table 7- Fair Premiums (Y) under Alternative Values of βRisk β =0.13

β

Y (%)

0.00

2.71

0.05

2.70

0.13

2.68

0.15

2.679

0.18

2.678

0.21

2.672

0.25

2.66

0.30

2.65

0.35

2.64

0.40

2.63

0.45

2.62

0.50

2.61

0.55

2.60

- The fair premiums for the base case are in bold face.

A higher value of risk-adjusted discount rate for UI payments leads to a lower fair premium. The β risks could therefore be negatively related to the fair premium.

Summary, Conclusion and Suggestion

Summary

The principal purpose of the unemployment insurance (UI) program is to provide workers with a safety net in the event that they lose their job. However, some worry that unemployment insurance benefits may inhibit unemployed workers from vigorously looking for or accepting a new job.

This study, for the first time, introduces the survival analysis of the unemployment duration to the unemployment insurance pricing model to measure the fair premium rate for unemployment insurance in Iran.

A Weibull distribution is adopted to estimate the average unemployment duration in computing the expenditure of UI benefits. For this purpose, we use the mean and variance of the Weibull distribution for measuring the related parameters.

And the CAPM-based insurance pricing framework is then applied to compute the fairly-priced premium rate for the UI program.

Conclusion

Since we have two amount for , we found two rate for UI based on real data. First we consider the case of married people, because of that the UI rate for this case is greater than the case of singe people. And in the case of married people, we consider the greatest benefit payment amount of the claimant’s insured earnings, which is equals to 80% of insured earning. So the fair premium rate which is calculated is maximum amount of UI rate.

For case of β=0.1 , the fair premium rate is equals to 0.0266 and for the case of β= 0.27 , this rate is equals to 0.0268.

As we seen, the fair premium rate that we calculated is much less than 4% which is the premium rate that government considers for UI premium rate in Iran.

[1]- Assistant Professor, ECO College of Insurance, Allameh Tabataba'i University.

[2]- ECO College of Insurance, Allameh Tabataba'i University.

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