Economic Sciences / 8. Mathematical Methods in Economics.

Master of Mathematics, Master of Management Omarova М.Т., Master of Economic Sciences Tyngisheva А.М.

Karaganda Economic University, Kazakhstan

THE INFLUENCE OF INSURANCE PREMIUMS ON ASSETS OF INSURANCE COMPANIES WITHIN ALMON’S METHOD.

Kazakhstan's insurance market is one of the fastest-growing markets of the CIS. In recent years there has been an evidence of positive trend in estimated figures of the insurance market, insurance companies' assets in particular, in the Republic of Kazakhstan. The following factors have contributed to the rapid growth of assets: 1) high rates of increase in the insurance premiums; 2) low rates of loss; 3) gradual capitalization of insurance companies; 4) increase in the number of insurance companies, including state and foreign participation; 5) changes in accounting for insurance reserves and reinsurer's share; 6) the use of the profit on the development of the insurance organization, rather than on paying dividends to shareholders [1].

In the given paper, we shall consider the influence of “insurance premiums’ growth” factor on the increase of assets as a whole while using the Almon’s method.

In the study of relationships between indicators as well as in the analysis of their development during the time, not only the instantaneous values of variables are used

time “t” itself. Models of this type are known as dynamic or temporal. In turn, the variables, influence of which is characterized by a certain time lag, are called variable lags. There are a number of reasons for the presence of lags in the economy; the following ones can be distinguished among them:

_{- Psychological reasons. These reasons are usually expressed in terms of inertia in human’s behavior. For example, people spend their income gradually rather than instantly. Getting used to a certain way of life leads to the fact that people get the same benefits for some time even after the fall of their real income;}

_{- Institutional reasons. For example, contracts between firms as well as labor contracts require certain constancy within the time of the contract (agreement), etc. [2].}

        _{The Almon’s model is based on the assumption that the “weightings” of the β1coefficients in the model can be approximated by polynomials of a certain extent of the j lag:}

Supposing that, than it can be represented by:

_{By setting we have:}

_.

Values, may be determined by OLS.

The procedure for applying the Almon’s method for calculating the parameters of the distributed lag model is as follows:

1. Maximum value of the lag is determined.

2. The polynomial degree describing the structure of the lag is determined.

3. Values of the variables are calculated.

4. The parameters of the linear regression equation are defined.

5. Parameters of the original distributed lag model are calculated.

By this means, we determine the impact of insurance premiums on the size of assets of insurance companies by using this method [3].

Table 1. The dynamics of assets and premiums of insurance companies.

Year	Assets mln.	Insurance premiums mln.
2000	8 382,0	8630,1
2001	15768,4	13873,5
2002	22419,0	22642,0
2003	20700,0	28870,0
2004	44100,0	39978,1
2005	73 346,3	67 123,1
2006	135 489,7	120 265,9
2007	223 556,1	147 343,3
2008	268822,9	133487,6
2009	297252,5	113289,7
2010	343 234,4	139 963,9
2011	387672,0	175 528,7
2012	442647,7	211 513,1
Note - data taken from the Financial Supervisory Committee reports of the National Bank of the Republic of Kazakhstan

We shall construct a model of distributed lag method for l=3:

Assuming that the lag structure is described by a second degree polynomial:

_,

For calculating the parameters of this model it is necessary to transform the original data into new variables :

,

_,

_.

Table 2. Converting the data into new variables.

Year	Assets()	Insurance premiums)	z0	z1	z2
2000	8382	86301
2001	15768,4	13873,5
2002	22419	22642
2003	20700	28870	151686,5	309292	854845
2004	44100	39978,1	105363,6	115774,5	244299,5
2005	73346,3	67123,1	158613,2	165644,1	359236,1
2006	135489,7	120265,9	256237,1	233689,3	486865,5
2007	223556,1	147343,3	374710,4	374446,4	748561,2
2008	268822,9	133487,6	468219,9	589244,4	1232515
2009	297252,5	113289,7	514386,5	788971,9	1805254
2010	343234,4	139963,9	534084,5	822294,8	1973330
2011	387672	175528,7	562269,9	767006,1	1794511
2012	442647,7	211513,1	640295,4	795325,6	1754992
Note - Compiled by authors based on Table 1

Calculation of the parameters of the regression equation by ordinary least squares for the selected values in the table, leads to the following results:

-73544,41223 + 1,186828 - 0,7836504+ 0,212455.

The equation of regression is statistically significant and so do all the regression coefficients in variables.

We shall find the coefficients of the original model by the formulas:

, , , .

Hence, the original distributed lag model is as follows:

=-73544,41223 + 1,186828 + 0,6156326 + 0,4693472 + 0,7479718

Analysis of the model shows that an increase in insurance premiums of 1 million tenge will lead to an average increase in assets up to 1,186,828 tenge.

As insurance premiums increase, the growth in total volume of assets will be 1.802.460, 6 tenge in a year, in two years it will show an increase of 2.271.807, 8. The increase of insurance premiums of 1 million tenge will lead to increase in the volume of assets up to 3.019.779, 6 in three years.

Hence, 39.3% of the total increase in assets is currently in progress; 20.4% - in one year; 15.5% - in 2 years; 24.8 – in 3 years.

Average lag of the model is:

= 0*0,393 + 1*0,204 + 2*0,155 + 3*0,248 = 1,258.

_{The magnitude of lag of 1, 3 years confirms that the significant part of growth effect of the insurance premiums is evidenced after the first year.}

_{Consequently, the Almon’s method model shows a direct dependence of assets on insurance premiums.}

Literature

1. The Abstract. Mayanlaeva. GI Insurance market of Kazakhstan: theory, practice and development imperatives.
2. Boroditš SA Econometrics textbook. - M.: New Knowledge, 2001. - 408.
3. Data analysis and forecasting of the economy: Textbook / N. Emelina. - Karaganda Economic University, 2011. - 111c.