Gábor Regősa: Consequences of the Insurance Intermediary commission’s Smoothing

Corvinus University of Budapest, 1093 Fővámtér8., Budapest, Hungary, , +3614825250

The paper investigates the consequences of a regulation prescribing that commission of insurance intermediaries should be paid smoothly, as a function of the arriving insurance premiums instead of paying a high acquisition commission at the beginning of the contract and only smaller commissions later. The regulation’s effects are investigated with a model and its simulation. As a result we obtain that after the intervention income of the decreasing number of intermediaries staying on the market will increase, number of intermediaries leaving the market decreases, and the ones staying on the market will have a better ability to gain consumers compared to the original case.

1.Introduction

The paper investigates the effects of a policy intervention on the insurance intermediary market. The intervention means that the different intermediaries (agents and brokers) would receive their commission on a different way as nowadays.

Distribution of most insurance products and one part of the banking products happens through a quite special distribution channel as it is presented by von DahlenandNapel (2004) and Cummins and Doherty (2006). Insurance companies apply intermediaries to sell their products. There are two types of intermediaries: agents, who sell the products of one more insurance companies and are entrusted by them and brokers who look for the products that are the most appropriate from the offer of one or more insurance companies for the consumer. But according to Eckardt (2002) this difference has no effect on the service’s quality. Intermediaries have a role not only in the sale of the product but also in informing customers: they have an important role in decreasing information asymmetry and transaction costs (Eckardt2002). Von Dahlen and Napel (2004) also analyze why insurers apply such distribution channels. They find three reasons: economies of scale, promotion of finding customers and decrease of customer acquisition’s risk. But this distribution channel has also disadvantages for insurance companies: intermediaries’ costs can be important (Brennan 1993, Banyár and Regős 2012). Efficiency of intermediation in financial markets was analyzed by Oduor et al. (2011) through the example of Kenya.Koutsomanoli-Filippaki et al. (2009) analyzed structural reform’ effects on banks’ and non-banking financial sector’s profit efficiency.

On the insurance market we can find not only short-term but also long-term contracts. Nowadays in case of such insurance or credit contracts intermediaries receive a high commission after contracting (its value can be more than the contract’s value at the first 2-3 months) and only a small commission later. It means that intermediaries are stimulated to obtain a large number of contracts and not to obtain such contracts that are viable in the long run, so the premium of which can be paid also some years later. This situation can also have unpleasant macroeconomic consequences in the long run: it was one of the causes of the crisis beginning in 2008 as presented by Sinclair et al. (2009). Connection between financial markets’ development and economic growth has been widely discussed nowadays: see e.g. Abu-Bader and Abu-Quarn (2008) or Yang and Yi (2008). The analyzed intervention’s purpose is to change this practice.

The paper investigates what happens if the state prescribes to insurance companies that they should pay commissions smoothly. We search the answer for the four following questions applying a model and a simulation:

  • How does the average age of intermediaries on the market change as a result of the regulation?
  • How does the average profit of intermediaries change as a result of the regulation?
  • How does the number of intermediaries who stay on the market and who leave the market change as a result of the regulation?
  • What will the staying intermediaries’ ability to get customers look like as a result of the intervention?

Besides we also prepare a sensitivity analysis investigatinghow the fluctuations in the intermediaries’ performance change the reform’s effects. Inthe model we assume as a short-run assumption that the analyzed market (which can be an insurance or a credit market) is saturated, so there are enough intermediaries on the market to find the potential customers. In the literature several authors (Nigh 1991, Dumm and Hoyt 2003, Campbell et al. 2003,Fearon and Philip 2005and Okura and Yanese 2010) find evidence that insurance markets are saturated. An example to such an insurance market is the motor third party liability (MTPL) market: number of cars determines demand for insurance: its total number will not increase if insurance companies employ twice as many intermediaries. As a previous paper (Banyár and Regős 2012) presented, life insurance market is also similar: people buy life insurance in some given situations, it cannot be influenced significantly by increasing the intermediary number. Market of retail credits can also be similar: after a given number of intermediaries, employing more will not increase the market size as potential customers will already be reached. This paper also showed in an oligopolistic framework that insurance companies employ more intermediaries than necessary due to the competition which leads to an increase in their costs and to a decrease in their profits. A possible way to analyze the insurance intermediary market is to apply game theory. Among such models we can find both sequential games (Bolton et al. 2007, Schiller 2009, Focht et al. 2009) and simultaneous games (Okura 2010a, 2010b). Hofmann and Nell (2008) prepared a Hoteling-model to compare the effects of the different remuneration systems: the commission-based one (paid by the insurer) and the fee-based one (paid by the consumer).

Section 2 presents the model, section 3 analyzes the policy intervention’s effects with the model, section 4 presents a sensitivity analysis while section 5 concludes and presents some policy implications.

  1. The Model

Intermediaries have two types of customers in each period. One type is the new customer and in the base setting the intermediary receives a commission ofqtafter such a customer. The other type is the customer obtained in the previous period (its number is already given in period t) after which the intermediary receives a commission of Qt.It means that contracts live for two periods by assumption. Inthe base setting qtis much higher than Qt. After the regulation’s introduction let the commission of the new contracts bert, and that of the old onesbe Rt. Assume thatqt+Qt=rt+Rt, so the sum of the two commissions is the same (no discounting), butqt-Qtrt-Rt, so inthe new system commissions are paid smoothly. It is also assumed that the market is saturated, thus total number of contracts does not depend on the number of intermediaries.

Further notations:

  • st: share of an intermediary from the total market in period t.
  • Total number of contracts: N (assumed to be constant in time)
  • Number of intermediaries on the market in period t:kt
  • Living cost of an intermediary: c (assumed to be constant in time)

Model’s operation is the following: there are some intermediaries on the market in each period, and it turns out according to it that how many contracts they have. Number of contracts in the given and in the previous periods determine the income of the intermediaries. If this value is more than the intermediary’s living cost, he stays on the market, unless he exits and looks for another job or starves to death – it is the same from our point of view. Applying this information, the unlimited number of unemployed decides whether they want to work as an intermediary inthe following period or not. As many unemployed enter to the market as many are expected to be able to cover their costs – regarding that they will have only new customers and they will receive commissions only after them.

2.1.Deterministic Model

In this model we have some further assumptions: intermediaries are identical: their costs and features are the same: they obtain the same share of the market in each period. We keep the original assumption that a new contract brings more commission than an old one. Equations of the model are the followings:

  1. Income of an old intermediary:

,

whereInctdenotes income in period t.

  1. Market share of an intermediary in period t:
  1. Market share of an intermediary in period t-1:
  1. Barrier to entry (if it holds, new intermediary enters):
  1. Barrier to exit (if it holds, the intermediary exits):

Substituting the market share into the above equations the followings are received:

  1. Income of an old intermediary:
  1. Barrier to entry (if it holds, new intermediary enters):
  1. Barrier to exit (if it holds, the intermediary exits):

Let see what happens inthe steady state. It can be seen that the barrier to entry will be effective in this case as if for someone it was good to entry, he has more income later (having customers from the previous period). Equations are the following inthis case:

The following variables are exogenous: c, q, Q, N, while the following ones are endogenous: s, Inc, k.

Solving the equations we receive:,,

We now analyze what happens when the new commission system is introduced. Assume that r=R. Old intermediaries on the market in the period after the regulation change receive Q after the old contracts and r after the new ones which is lower than q. As the system was in the steady state, and the new entrants’ situation worsened, no new entry happens. What happens to the old ones? Their income will be the following:

It means a decrease compared to the previous one as rtqt. Substituting the values of the steady state to the above equation and assuming the total number of contracts to be constant, we receive:

Intermediaries on the market exit if it does not cover their expenses, thus:

thus

As r=0.5(q+Q), it is the same as:

So, it depends on the measure of smoothing that whether everyone stays on the market or leaves it temporarily. If everyone left the market (not a too realistic conclusion), new entrants will arrive to the market until the barrier to entry becomes effective. In this case income of new entrants and the two other equations (assuming that they enter to the market in period t):

Number of new entrants is: , so number of intermediaries working onthe market decreased.

2.2.Stochastic Model

Investigation of this case allows making difference among intermediaries according to their performance. We assume that each intermediary has different abilities and that their performance fluctuates every year. Equations are now the followings:

  1. Income of an old intermediary:

,

whereInctidenotes the income of intermediary i in period t.

  1. Market share of intermediary i in period t:

wherepiis the point value of intermediary i. pi is assumed to be normally distributed with an expected value of aiand with a variance of σ2– assumed to be constant. This random variable represents the intermediary’s performance in the given period, so its value changes each period. ai is assumed to be uniformly distributed onthe interval (0,a). It represents the intermediary’s skill. Its value is determined when the intermediary enters to the market, butit is not known by the intermediary. Further equations are the followings:

  1. Market share in period t-1 – already determined inthe previous period.
  2. Barrier to entry (if it holds, new intermediary enters to the market):
  1. Barrier to exit (if it holds, the intermediary stays on the market):

In equation 4 E() denotes the expected value. We assume that living costs and market size are constant, thus ct=ct+1=candNt=Nt+1=N. At the moment of the decision about entering to the market, new entrants know the number of intermediaries leaving the market and they decide whether they want to enter or not.

New intermediary’s skill parameter has an expected value of 0.5a. Intermediaries outside the market do not know the a parameter of intermediaries on the market, or what’s more, it is also possible that intermediaries on the market do also not know their own parameter. So, new intermediaries expect that each intermediary’s expected ability parameter is 0.5a. This assumption can seem to be strong at the first sight but a huge number of new intermediaries can be found on the market in each period which proves that people outside the intermediation market think that they can do this work as good as the old.

In this case the expected market share is

so everyone expects to receive the same share of the market, there is no learning inthe model.

Expected income of new intermediaries:

Entrance condition is that it should be higher than their costs:

Rearranging it:

3.Effects of policy intervention

We prepare a simulation to analyze the policy intervention’s effects without applying the data of a concrete country as it would exceed the calculation capacities. Despite, it can be declared that the equation to the number of intermediaries holds more or less to the Hungarian data.

During the simulation the following parameters are applied: q=7.7, Q=2.3, N=1500, C=60, σ=1.5, a=10. From the beginning of the simulation (when everyone is new on the market) 200 periods were considered with and without policy intervention period 100. Simulation was run 1000 times and the average of the received values was analyzed according to the criteria detailed in the introduction. In the model there will be 192 intermediaries without the regulation and after the regulation’s introduction (r=R=5 from period 100) it will decrease to 125 and intermediaries with a worse performance leave the market.

3.1.Intervention’s effect on the average “age” of intermediaries on the market

Figures 1 and 2 show the average age of intermediaries on the market (so, the number they spent on the market) as the average of 1000 simulations without regulation and with regulation.

Until period 100 of course the same happens in both cases: the average age increases but in a decreasing degree (concave function). Its reason is that a new intermediary decreases the average age more next to a higher average age than at a lower one. When the regulation is introduced in period 100, average age of intermediaries increases suddenly (a lot of intermediaries leave the market but not the oldest ones with better experience and ability parameter) but after it returns to a value between this one and the original one and after increases more than it would without the regulation. It means that intermediaries after the regulation’s introduction change inthe market less than they would without the regulation, they work in average on the intermediary market more than without regulation.

Figure 1: Average time spent onthe market by intermediaries without regulation

Figure 2: Average time spent onthe market by intermediaries with regulation

3.2.Intervention’s effect on average profit of intermediaries

Figures 3 and 4 show the average surplus of intermediaries staying onthe market, thus difference of their incomes and costs.

At the beginning of both simulations profit takes a higher value after a lower one in period 0 (as in this period there are no old customers, intermediaries can receive commission only after the new ones). Later this value decreases and converges to a certain level. It means that at the beginning of the simulation staying intermediaries have higher incomes than later as there are more intermediaries leaving the market (worse intermediaries).

After regulation’s introduction, surplus in period 100 decreases (as the total commission decreases) and after two periods it will have a higher value compared to the original one. Its reason is that the distributed commission does not change but there are fewer intermediaries, so the regulation increases the staying intermediaries’ welfare.

Figure 3: Average surplus of intermediaries staying on the market at the end of the periods without regulation

3.3.Intervention’s effects on number of intermediaries staying on the market and leaving it

Figures 5 and 6 show the average number of intermediaries staying on the market while figure 7 and 8 show the average number of intermediaries leaving the market. Without the regulation we see a slow increase in the number of staying intermediaries and a decrease in the number of the leaving ones: by the end about 25 intermediaries leave the market from 192 in each period.

Figure 4: Average surplus of intermediaries staying on the market at the end of the periods with regulation

Figure 5: Average number of staying intermediaries at the end of the periods without regulation

Figure 6: Average number of staying intermediaries at the end of the periods without regulation

Figure 7: Average number of leaving intermediaries at the end of the periods without regulation

Figure 8: Average number of leaving intermediaries at the end of the periods with regulation

After the regulation number of intermediaries staying on the market decreases, and after a small increase reaches a new equilibrium which is lower than the original one. In this case number of intermediaries leaving the market will be low (almost 0), and the market will be more stable than without the regulation. So, regulation results a more stable intermediary market: number of new intermediaries and leaving old intermediaries decreases.

3.4.Intervention’s effect on the average skills of intermediaries

Figures 9 and 10 show the average skill parameter of intermediaries staying on the market (ai).At the beginning the parameter’s value increases continuously but in a decreasing degree. It does not reach 9 even until period 200 without regulation but with the policy intervention it takes a higher value in period 100 and after it has a lower value, but it will be more than without regulation. It means that due to the regulation intermediaries with better consumer collecting ability stay onthe market, thus, in the model average of the skill parameter increases significantly.