GÁBOR REGŐSA: CONSEQUENCES OF THE INSURANCE
INTERMEDIARY COMMISSION’S SMOOTHING
Corvinus University of Budapest, 1093 Fővám tér 8., Budapest, Hungary, [email protected],
+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 Dahlen and Napel
(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 (Eckardt 2002). 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 investigating how the fluctuations in the
intermediaries’ performance change the reform’s effects. In the 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 2005 and 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.
2. 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 of qt after 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. In the base setting qt is much
higher than Qt. After the regulation’s introduction let the commission of the new
contracts be rt, and that of the old ones be Rt. Assume that qt+Qt=rt+Rt, so the sum of the
two commissions is the same (no discounting), but qt-Qt>rt-Rt, so in the 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 in the 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:
𝑠𝑡 𝑁𝑡 𝑞𝑡 + 𝑠𝑡−1 𝑁𝑡−1 𝑄𝑡 = 𝐼𝑛𝑐𝑡 ,
where Inct denotes income in period t.
2. Market share of an intermediary in period t:
𝑠𝑡 =
1
kt
3. Market share of an intermediary in period t-1:
𝑠𝑡−1 =
1
k t−1
4. Barrier to entry (if it holds, new intermediary enters):
𝑐𝑡+1 ≤ 𝑠𝑡+1 𝑁𝑡+1 𝑞𝑡+1
5. Barrier to exit (if it holds, the intermediary exits):
𝑐𝑡 > 𝑠𝑡 𝑁𝑡 𝑞𝑡 + 𝑠𝑡−1 𝑁𝑡−1 𝑄𝑡
Substituting the market share into the above equations the followings are received:
1. Income of an old intermediary:
𝑁𝑡
𝑁𝑡−1
𝑞𝑡 +
𝑄 = 𝐼𝑛𝑐𝑡
𝑘𝑡
𝑘𝑡−1 𝑡
2. Barrier to entry (if it holds, new intermediary enters):
𝑐𝑡+1 ≤
𝑁𝑡+1
𝑞
𝑘𝑡+1 𝑡+1
3. Barrier to exit (if it holds, the intermediary exits):
𝑐𝑡 >
𝑁𝑡
𝑁𝑡−1
𝑞𝑡 +
𝑄
𝑘𝑡
𝑘𝑡−1 𝑡
Let see what happens in the 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 in this case:
1. 𝑠𝑁(𝑞 + 𝑄) = 𝐼𝑛𝑐
1
2. 𝑠 = 𝑘
3. 𝑐 =
𝑁𝑞
𝑘
The following variables are exogenous: c, q, Q, N, while the following ones are
endogenous: s, Inc, k.
Solving the equations we receive: 𝑘 =
𝑁𝑞
𝑐
𝑐
,𝑠 = 𝑞𝑁, 𝐼𝑛𝑐 =
𝑞+𝑄
𝑞
𝑐
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:
𝑠𝑡 𝑁𝑡 𝑟𝑡 + 𝑠𝑡−1 𝑁𝑡−1 𝑄𝑡 = 𝐼𝑛𝑐𝑡
It means a decrease compared to the previous one as rt<qt. Substituting the values of the
steady state to the above equation and assuming the total number of contracts to be
constant, we receive:
𝑐𝑡
(𝑟 + 𝑄𝑡 ) = 𝐼𝑛𝑐𝑡
𝑞𝑡 𝑡
Intermediaries on the market exit if it does not cover their expenses, thus:
𝑐𝑡
(𝑟 + 𝑄𝑡 ) < 𝑐𝑡 ,
𝑞𝑡 𝑡
thus
(𝑟𝑡 + 𝑄𝑡 )
<1
𝑞𝑡
As r=0.5(q+Q), it is the same as:
𝑄
< 0.5
𝑞
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):
𝑠𝑡 𝑁𝑡 𝑟𝑡 = 𝐼𝑛𝑐𝑡
𝑠𝑡 =
1
kt
𝑐𝑡 = 𝐼𝑛𝑐𝑡
Number of new entrants is: 𝑘 =
𝑁𝑟
𝑐
, so number of intermediaries working on the 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:
𝑖
𝑠𝑡𝑖 𝑁𝑡 𝑞𝑡 + 𝑠𝑡−1
𝑁𝑡−1 𝑄𝑡 = 𝐼𝑛𝑐𝑡𝑖 ,
where Incti denotes the income of intermediary i in period t.
2. Market share of intermediary i in period t:
𝑠𝑡𝑖 =
pi
∑kj=1 pj
where pi is the point value of intermediary i. pi is assumed to be normally distributed
with an expected value of ai and 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 on the interval
(0,a). It represents the intermediary’s skill. Its value is determined when the
intermediary enters to the market, but it is not known by the intermediary. Further
equations are the followings:
3. Market share in period t-1 – already determined in the previous period.
4. Barrier to entry (if it holds, new intermediary enters to the market):
ú𝑗
E(𝐼𝑛𝑐𝑡+1 ) ≥ 𝑐𝑡+1
5. Barrier to exit (if it holds, the intermediary stays on the market):
𝐼𝑛𝑐𝑡𝑖 , > 𝑐𝑡
In equation 4 E() denotes the expected value. We assume that living costs and market
size are constant, thus ct=ct+1=c and Nt=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
𝑖
E(𝑠𝑡+1
)=
1
no. of old intermediaries + no. of new intermediaries
so everyone expects to receive the same share of the market, there is no learning in the
model.
Expected income of new intermediaries:
1
Nr
no. of old intermediaries + no. of new intermediaries t t
Entrance condition is that it should be higher than their costs:
1
Nr >𝑐
no. of old intermediaries + no. of new intermediaries t t
Rearranging it:
Nt rt
− no. of old intermediaries > no. of new intermediaries
c
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 in the 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 on the market by intermediaries without regulation
Figure 2: Average time spent on the 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 on the 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 on the market, thus, in the
model average of the skill parameter increases significantly.
Figure 9: Average skill parameter of intermediaries staying on the market without regulation
Figure 10: Average skill parameter of intermediaries staying on the market without regulation
4. SENSITIVITY ANALYSIS
We now analyze whether the above presented results are sensitive to a change in the σ
parameter, so whether the performance’s variability influences the policy intervention’s
effect. At the sensitivity analysis the average value of the analyzed variables are
presented in period 199 as a function of σ.
4.1.
SENSITIVITY ANALYSIS TO THE AVERAGE “AGE” OF INTERMEDIARIES ON THE
MARKET
Figures 11 and 12 show the average age of intermediaries on the market in period 199
with and without regulation as a function of the volatility parameter. Without regulation
we can find a reverse logistic curve: at low volatility intermediaries who entered the
market and who can stay there will be there also in the long run but at high volatility,
they leave the market with a higher probability. Regulation decreases this variable’s
range: while without regulation age takes values between 0 and 200, with regulation it
takes values only between 60 and 150. The function’s form is also quite special here. So,
average time spent on the market by the intermediaries and the intervention’s effect on
it are influenced by their performance’s volatility.
Figure 11: Average time spent on the market by intermediaries without regulation as a function of sigma
4.2.
SENSITIVITY ANALYSIS TO THE AVERAGE PROFIT OF INTERMEDIARIES
Figures 13 and 14 show the average surplus of intermediaries staying on the market in
period 199 without and with regulation. Without regulation, the surplus increases
continuously if sigma increases. With regulation surplus almost remains constant at low
sigma and after a small decrease it increases. In this case due to the less intermediary on
the market, surplus will always be higher than in the case without regulation, so,
regulation’s effects are not significantly influenced here by the σ parameter.
Figure 12: Average time spent on the market by intermediaries with regulation as a function of sigma
Figure 13: Average surplus of intermediaries staying on the market in period 199 without regulation as a
function of sigma
Figure 14: Average surplus of intermediaries staying on the market in period 199 with regulation as a
function of sigma
4.3.
SENSITIVITY ANALYSIS TO NUMBER OF INTERMEDIARIES LEAVING THE MARKET
Figures 15 and 16 show the average number of intermediaries leaving the market in
period 199. Number of staying intermediaries is strongly related. Both without and with
regulation, number of leaving intermediaries increases if σ increases but the function’s
form is a bit different: with regulation sharp increase of leaving intermediaries begins at
a higher σ, and functions’ types are also different. With regulation number of leaving
intermediaries is always lower than without regulation, so, σ has only little influence on:
regulation’s introduction always decreases the number of leaving intermediaries.
4.4.
SENSITIVITY ANALYSIS TO THE AVERAGE SKILLS OF INTERMEDIARIES
Figures 17 and 18 show the staying intermediaries’ average skill parameter in period
199. Without regulation this function will have a maximum where sigma is about one.
With regulation next to the global maximum at σ=1.5 we can also find a local maximum
at σ=0.2. With regulation the parameter’s value is usually (but not always) higher than
without regulation, so, policy intervention’s effects are only a bit sensitive to the σ
parameter, in most cases regulation’s introduction results that average skill parameter
(ability to obtain consumers) will be higher than without the regulation.
Figure 15: average number of leaving intermediaries in period 199 without regulation as a function of sigma
Figure 16: average number of leaving intermediaries in period 199 with regulation as a function of sigma
Figure 17: Average value of the skill parameter in period 199 without regulation as a function of sigma
Figure 18: Average value of the skill parameter in period 199 with regulation as a function of sigma
5. CONCLUSION AND POLICY IMPLICATIONS
The paper investigated with a model and its simulations the effects of a regulation which
would prescribe the smoothing of commissions on the insurance intermediary market.
In the current system, insurance companies pay a high commission at the beginning of
the contract but after only a lower one.
According to our results, after the regulation’s introduction average time spent on the
market by the intermediaries increases besides the base parameters but it can also
decrease if the parameter describing the volatility of the intermediaries’ performance
changes. Profit of intermediaries increased after the regulation independently from the
parameter describing their performance’s volatility. Number of intermediaries leaving
the market and staying there decreased some periods after the regulation’s introduction
for all values of the performance-volatility parameter. As a result of the regulation less
intermediaries stayed on the market, but in general their ability to obtain consumers
was better.
From the policy’s point of view appropriate operation of the financial intermediation
market (including the insurance and credit intermediation) is fundamental in order to
avoid negative macroeconomic consequences. Non-smoothed commissions have already
had some negative consequences – see for example the recent credit bubble. So, a
smoothed commission could also lead to more sustainable contracts both on the credit
market but also in case of the insurances (e.g. life insurance) – although in the paper we
did not deal with the quantity of quality of contracts.
As our model revealed, smoothing of commissions would lead to a more stable
intermediary market: although there would be less intermediaries in the market, their
fluctuation would be not so intensive. From the policy’s point of view it can be useful:
nowadays many new intermediaries think to be successful on the intermediation
market, enter there, but leave the market soon as they could not obtain enough new
contracts, so, for them their work is just a waste of time – the regulation could possibly
also diminish this phenomenon.
So, our policy implication is that it worth regulating the commissions, it can lead to a
more stable intermediary market and it can help to avoid some negative consequences
that can appear on the insurance or credit market.
ACKNOWLEDGEMENT
The author would like to thank József Banyár for valuable suggestions.
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