APPLICATION OF DISCRIMINANT ANALYSIS TO THE EVALUATION AND FORECASTING OF ECONOMIC SITUATION IN POLAND

Joanna Kisielińska, Urszula Skórnik-Pokarowska

ABSTRACT

This paper describes the indicators of the present and future economical situation. The discriminant analysis has been used. The real income increase, gross fixed capital formation and low USD/PLN exchange rate are the good prosperity indicators. The next year prosperity is indicated by high increase of the gross fixed capital formation, high current account and budget deficit values (as GDP %) and decreases of the private and public consumption expenditure, export and low unemployment rate at the end of the year.

Key words: discriminant analysis, macroeconomic indicators.

INTRODUCTION

A proper evaluation of the economic situation of a given country is necessary for undertaking measures, which would improve or at least maintain the underlying tendency. For a general evaluation of the economic situation the fundamental criterion is the gross domestic product (“GDP”) growth rate. A thorough analysis should however take into consideration a whole range of additional macroeconomic indices.

The aim of the research presented in the article was to distinguish relevant indices from the vast range of indices that determine the economic situation or that influence the evaluation process and enable forecasting of its further state. Those indices can be a base for a construction of current and future conjuncture barometers.

The goal set was achieved by application of discriminant analysis method, which is one of many multivariate data analysis methods applied in cases where an object is described by many indices. The set of indices can be divided into disjoint classes, based on which, a discriminant function is constructed. Further, the values of the discriminant function allow to determine to which class a given object should belong to. Indices play the role of independent variables. The description of this method can be found in the papers by Grabiński, Jajuga and others [6,7,8]. The methods shown there allow constructing linear discriminant functions (“LDF”).

The research shown in the paper covers the period 1991 – 2002, which was divided into two disjoint classes, namely (i) years of the upturn of Polish economy and (ii) years of economic downturn. The split into two classes was based on the GDP’s growth rate. For the division obtained in that way the discriminant function was constructed based on the sets of macroeconomic financial indices.

The method of discriminant analysis allows to distinguish and rank those indicators that are responsible in the most significant way for the differences between the objects and simultaneously for division into classes. The discriminant function calculated in the paper based on macroeconomic indicators can be applied to both evaluation and prediction of the economic situation. It is therefore a barometer of the present or future (following year) economic situation.

The calculations were made with support of the STATISTICA and the data was sourced from the Polish Official Statistics (POS) (shown in Annual Statistics and Information Bulletins of National Bank of Poland - the bulletins are published periodically and on web sites of NBP).

MACROECONOMIC INDICES THAT BUILD THE BAROMETERS OF POLISH ECONOMY SITUATION

The evaluation of the economic situation of Poland in the late 90’s can be found in the collective work edited by Lipiński and Orłowski [9]. The authors analyse the influence of the domestic and foreign situation on the rate of the economic growth. Thorough attention was given to the problems related to domestic and exterior demand, equip of Polish economy in production factors and their use, structure of capital investments, state of public finances, state of financial sector (especially commercial banking), and fiscal and monetary policy.

In our work we have also taken into consideration the exterior indices that influence Polish economy such as the globalisation process, the development of global economy, trade and current account balance. The search of barometers of economic situation and the study of Polish economy monitoring system can be found in a collective work edited by Matkowski [10]. To a large extend the research described there was based on the experiences of Western Europe countries, where such systems successfully exist. It is however not possible to transfer directly the patterns worked there, as they require adopting to Polish conditions. In the work a thorough attention was given to methodological questions, especially to a problem of distinguishing a trend or a periodic oscillation from the given time dependence. Our final aim was to find a collection of synthetic coefficients that constitute the searched barometers of economic situation. The indices were divided into two groups - quantitative coefficients and qualitative. Quantitative barometers are built based on statistical data, which comprise over a hundred features, gathered in time series. They contain information about industrial production output in construction sector, agriculture, transportation and retail. Data connected with capital investment expenditures, budget income and expenditures, inflation, import and export, employment and unemployment, supply of money, current account balance and foreign exchange rate make up the next group.

The quantitative indices were measured based on questionnaire research made by POS among enterprises of processing industry, construction and trade. The data were replenished by indices of social mood and stock exchange indices.

Barczyk and Kowalczyk [2] apply the method of indices to investigate the oscillation of economic situation. They also distinguished quantitative indices that are constructed based on the information that comes from the special test method (which in fact is a kind of questionnaire done among economic subjects).

The most important factor here is the GDP, divided into private consumption and gross consumption, accumulation (the rate of growth of gross capital) and surplus of export over import (balance of trade). Many macroeconomic indices were used by authors in the macroeconomic models they have built.

Chojna, Jagiełło and Marczewski [3] on the other hand show a set of 14 macroeconomic indices, which they called “basic” and make a fundamentals for the evaluation of the economic situation in Poland in 2000 and the forecasting for 2001. This set of indicators embraces GDP, household and public consumption, gross capital formation, export of goods and services, import of goods and services, average monthly gross salaries, household savings rate, unemployment rate, average refinance credit rate, current account balance, budget deficit, US dollar exchange rate in PLN. Some of those indices were shown as annual changes, some were compared to the GDP.

We have chosen the collection proposed by Chojna, Jagiełło and Marczewski [3] for our analysis as this set contains only 14 indices which build an exhaustive set of information about the economic situation in Poland.

MACROECONOMIC INDICATORS THAT BUILD A BASIS FOR CONSTRUCTION OF THE DISCRIMINAT FUNCTION

The Table 1 shows a collection of statistical data, which was used for determining the macroeconomic indicators needed for constructing the discriminant function. The notations used in the paper are consistent with that used by POS.

Since the fluctuation in value of PLN in the investigated period were considerable, it is necessary to chose one year as a basis. We have chosen the year 1990, and then calculations were made based on the inflation rate.

For some data, e.g., gross capital formation, other indices seem to be more relevant (e.g., the index of capital formation). Since the relations between the data from the same year should not be changed it is necessary to apply a common conversion rate.

Only the dollar exchange rate according to NBP has not been recalculated into constant prices, since its current value contains information about Polish economy.

The following macroeconomic indices were turned into constant prices and then the annual percentage changes were calculated:

• gross domestic product,

• individual household consumption,

• public expenditures,

• gross fixed capital formation,

• export of goods and services,

• import of goods and services,

• average monthly gross salary in real term.

The rate of unemployment is a rate taken at the end of the year. The savings rate has been calculated as a ratio of gross savings to nominal gross income of individual households. The inflation rate is an index of goods and services prices, the refinance credit rate is an average annual rate in a given year.

The budget deficit was calculated as a difference of gross income and expenditures compared to GDP. The current account balance was calculated into PLN and compared to GDP.

Average monthly salary is the net monthly salary since 1992. The Table 2 shows annual changes of salaries in real terms as stated by POS.

The final set of indices used for determining the discriminant function is contained in Table 2. Since many of them are annual percentage changes, the data comprise the period 1991-2001.

THE DISCRIMINANT FUNCTION BUILT FOR THE PURPOSE OF EVALUATION OF THE ECONOMIC SITUATION

The period between 1991 and 2001 was divided into two classes. The first class contains years of weak condition of the Polish economy in which the GDP growth was smaller than the average in this period (“Class I”) and the second consists of years, in which the GDP growth was greater than the average (“Class II”).

The division into two classes was made for the average of 1.58%. The years 1991, 1992, 1993, 2000 and 2001 belong to the class I, while the years 1994, 1995, 1996, 1997, 1998, 1999 belong to the class II. Further the linear discriminant function was calculated. Its task is to make a division into two classes basing on the economic indicators.

The calculations were made with the help of the step progress analysis of STATISTICA. In this method we introduce step by step to the model (i.e., to the discriminant function) those indicators, which determine most the classes.

The indicators that determine the values of the discriminant function are shown in Table 3.

Table 3 contains two kinds of coefficients of the discriminant function: raw and standardized. The raw coefficients allow to calculate the values of the discriminant function. The standardized coefficients that are related to the standardized variables allow to evaluate indices. The larger the absolute value of the standardized coefficient the larger the influence of that variable on the membership to a given class (the influence in Table 3 is reflected by the so called rank of the index).

The Class I contains years with negative values of the linear discriminant function, the Class II contains years for which the value of the discriminant function is positive.

The following macroeconomic indices influence in the most significant level the discrimination of the classes:

• Gross salary in real terms (annual changes in %),

• Gross fixed capital formation (annual changes in %),

• Average USD dollar exchange rate.

The coefficients of the LDF are positive in the case of gross salaries in real terms and gross capital expenditure while they are negative for US dollar exchange rate. One can say that the years with large GDP’s growth rate were characterized by large rate of growth of gross salaries in real terms and gross capital formation. Gross capital formation index is strongly correlated with import changes index (the coefficient of correlation equals 0.8). Hence, large GDP’s growth rate was accompanied by large import’s growth rate.

The US dollar exchange rate on the other hand is strongly correlated with inflation rate (the correlation coefficient is -0.93). That indicates that years with large rate of growth of the gross domestic product were characterized by low US dollar exchange rate (the coefficient of LDF is negative) and large inflation.

To evaluate the classification made with the help of the discriminant function one can also apply the Wilks lambda test statistics. In the above case its value is 0.21. This value indicates that the quality of the discrimination is high (Lambda Wilks statistics equal to 0 means a perfect discrimination power). This can also be confirmed by the classification matrix shown in Table 4.

In 100% cases of the investigated population a correct classification was achieved.

Linear discriminant function, which was determined by parameters in Table 3, can be applied to evaluation of the economic situation in Poland in 2002.

The macroeconomic indices for 2002 were calculated basing on data published by POS on the web page www.stat.gov.pl. The annual change of gross salaries in real in 2002 was 2.36%, while the annual change of gross fixed capital formation was -8.54%. Average US dollar exchange rate was 4.08 PLN. The value of LFD function for 2002 is -1.51, what means a weak condition of Polish economy. It coincides with the real situation.

As comparison we have the value of LFD for 2001 equal to -1.43. The evaluation for 2002 is worse than for 2001. The changes of the gross domestic product were 0.6% in 2001 while they were 1.4% in 2002. So the comparison of the economic situation in 2001 and 2002 based on the values of LDF indicates an opposite tendency than it was in reality. Since the existing differences are slight one can assume that the linear discriminant function makes a proper division of the considered period into classes.

DISCRIMINANT FUNCTION BUILT FOR PREDICTION OF THE ECONOMIC SITUATION

The construction of the linear discriminant function for the purpose of prediction of economic situation requires certain amendments in the pattern applied above. The criterion in this case is also the percentage GDP’s growth change. Since our task is forecasting, the change of GDP in percent should come from the year ahead of the one for that macroeconomic indices were calculated.

The increase of GDP for 1991 will not be used in construction of the LDF. It is however necessary to add data for the year 2002. The GDP growth in 2002 equalled 1.00% (GDP for 2002 was equal 771112.8 million PLN).

The division into classes was done based on GDP growth in a given year, while the discriminant function was constructed based on macroeconomic indices for the preceding year (in the period 1992 – 2002).

The class I contains years for which the increase of GDP was smaller than the average while class II consists of those years for which the increase of GDP was larger than the average. As a result class I consists of the years 1992, 1993, 2000, 2001 and 2002, while class II – 1994, 1995, 1996, 1997, 1998, 1999. Then the discriminant function was calculated. The task of that function is to make the division into classes basing on the macroeconomic indices.

The Table 5 shows raw and standardized coefficients of the discriminant function as well as ranks of macroeconomic indices useful fore forecasting purpose.

The discrimination of the classes was influence in the most significant level by:

• Gross capital expenditure (annual changes in %),

• Individual consumption (annual changes in %%),

• Export of goods and services (annual changes in %),

• Current account (GDP%),

• Public consumption (annual changes in %),

• Rate of unemployment (at the end of the year),

• Budget deficit value (GDP%).

Judging by the signs of the discriminant function LDF one can presume that the high increase of GDP in the next year is predicted by: high increase of gross fixed capital formation, high level of current account and high budget deficit, large decrease of public and private consumption, large decrease of export and small rate of unemployment.

The lambda Wilks statistics is equal 0.04, what implies very high quality of classification done by linear discriminant function. Alike in the previous case all years were classified correctly. The linear discriminant function described by parameters shown in Table 5 can be used for forecasting of the economic situation in Poland. The annual changes of gross fixed capital formation in 2002 were -8.54%, individual consumption was 1.37%, export of goods and services was 6.28%, and public consumption -0.91%. Current account built -3.55%, and a budget deficit was -5.11% as compared to GDP. The rate of unemployment was 18% at the end of the year.

The indicators were calculated basing on information provided on Polish web page of the Central Statistical Office [4].

The value of LFD for 2002 is –4.52, that indicates weak condition of the economic situation in Poland in 2003. This is consistent with the real state. The value of LDF in 2001 was -5.22. That means that the forecasting done for the year 2002 indicated worse situation than for 2003. Hence the comparison of forecasting done with the help of LDF reflects the reality. Namely, the general opinion confirms the fact that the economic situation in 2003 however bad it is it is better than in 2002.

CONCLUSIONS

The research shown above indicates that indicators that determine the evaluation of the present economic situation are annual changes of gross wages and salaries and gross fixed capital formation. In the years characterized as good the rate of growth of those indicators was large (that can be deduced from positivity of LDF coefficients). Also the US dollar exchange rate plays an important role in that process. High values of US dollar exchange rate indicate weak economic situation of the country (negative values of LDF).

The discriminant function (see Table 3) that is a barometer of the present economic situation is of the form:

LFD=0.108+0.432·RWB+0.081·NBNST-0.477·KUSD

where:

RWB - real income (annual changes in %),
NBNST - gross fixed capital formation (annual changes in %),
KUSD – average US dollar exchange rate in NBP.

If the value of the LFD is positive, then the economic situation is good. On the other hand negative values of LDF indicate weak economic situation.

For forecasting purpose it is useful to use changes of gross fixed capital formation, private consumption, export of goods and services, current account value (as GDP%), private consumption changes rate, rate of unemployment (at the end of the year) and budget deficit values (as GDP%).

The discriminant function (see Table 5) that is a barometer of the future economic situation is of the form:

LFD=24.94+0.69·NBNST-2.62·SPRYW-0.30·ETU+1.50·RB-0.35·SPUB+
-0.47·SB+0.91·DB

where:

NBNST - gross capital formation (annual changes in %),
SPRYW - individual consumption (annual changes in %),
ETU - export of goods and services (annual changes in %),
RB - current account (GDP%),
SPUB - public expenditures (annual changes in %),
SB - rate of unemployment (at the end of the year),
DB – budget deficit (GDP%).

If in a given year the value of LFD is positive, then the economic situation is favourable, negative on the other hand indicates weak condition of the economy.

Large increase rate of gross fixed capital formation, high values of current account (as GDP%), high values of budget deficit (as GDP%) on one hand and small values of rate of unemployment at the end of the year, decrease of private and public consumption, decrease of export indicate prosperity.

Both barometers of the present and future economic situation have high discrimination significance what can be confirmed by low values of lambda Wilks statistics.

The values of the discriminant function for the year 2002 give a proper estimation and forecasting of the economic situation in Poland. The comparison of the years 2001 and 2002 is consistent with reality in case of forecasting and wrong in case of evaluation.

REFERENCES

1. Annual Statistics POS 1991 – 2002. Central Statistical Office, Warsaw

2. Barczyk R., Kowalczyk Z., 1993. Methods of economic situation research. PWN, Warsaw – Poznan

3. Chojna J., Jagiełło M., Marczewski K., 2001. Economic situation in Poland (in) Marczewski K. (ed.): Economic situation of the world and Poland in 1999 – 2001. Foreign Trade Research Institute (IKCHZ), Warsaw

4. Data of Central Statistical Office (in) www.stat.gov.pl

5. Data of National Bank of Poland (NBP) (in) www.nbp.pl

6. Grabiński T., 1992. Methods of taxonometrics. Ed. Economic University, Cracow

7. Jajuga K., 1990. Statistic theory of images identification. PWN, Warsaw

8. Jajuga K., 1993. Multidimensional statistic analysis. PWN, Warsaw

9. Lipiński J., Orłowski W., 2001. Economic growth in Poland – medium-term perspective. Ed. House Bellona, Warsaw

10. Matkowski Z., 1999 (ed.). Barometers of economic situation for Polish economy. Warsaw School of Economics, Warsaw

Urszula Skórnik – Pokarowska
Department of Econometrics and Informatic
Warsaw Agricultural University
ul. Nowoursynowska 166, 02-787 Warsaw
e-mail: ula.skornik@plusnet.pl

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