This paper focus on exploring the relationship between income and consumption in Bulgaria and Russia over the period 19902010. We use gross national income (GNI) per capita as a proxy to represent income and household final consumption as a proxy to represent consumption. The long run relations are estimated by cointegration model. The results show that there are positive and significant long run relationships between GNI and consumptions for Bulgaria and Russia. It states that the consumption depend on income; a rise in income increases the consumption. In Bulgaria, the incomeconsumption relationship is more pronounced than in Russia.
Keywords: Consumption; Bulgaria, Russia, income, cointegration analysis
1. Introduction
Households increase their utility by consuming the produced goods and services. They increase their wellbeing by this major component of the aggregate demand. For this reason the possible determinants of the aggregate consumption function have been analyzed intensively in the economic literature.
The purpose of this study is to estimate incomeconsumption relationship for the Bulgaria and Russia using time series data from the World Bank group. The broad hypothesis being tested is that consumption is closely related to the level of current income. The hypothesis rests on idea that consumption is made possible on the amount of money available for spending.
2. Literature review
Consumption accounts a significant proportion of national income, hence it is a main factor to promote economic growth. Hence for this reason, exploring the relationship between consumption and income, generally labeled as consumption function has played main role in economic theory since Keynes introduced Absolute Income Hypothesis (AIH) from The General Theory.
2.1 Current income theories of consumption
The consumption function is about the functional relationship between consumption and income. It expresses the functional incomeconsumption relation and all its determinants. It is a single mathematical function used to express consumption expenditure, it can be written as:
C =f(Yd), where C= consumption and Yd=disposable income. The concept of the consumption function first formulated in Keynes’ book General Theory of Employment Interest and Money^{1} The function is used to calculate the amount of total consumption expenditure in an economy. It is consisted of autonomous consumption which is not affected by current income and induced consumption that is influenced by the economy’s income level. The simple function is written as the linear function:
Ct=α0+α1Ytd
Where:
Ct is the total consumption at time t
α0 is autonomous consumption, which represents consumption when income is zero. In estimation, it is assumed to be positive (α0>0)
α1 is the marginal propensity to consume (0<α1<1)
Ytd is disposable income at time t
Absolute income hypothesis:
Keynesian theory (1936), what is known as the Absolute Income Hypothesis (AIH), and postulates that the consumption level of a household only depends on its absolute level (current level) of income and ignores the potential future income. The hypothesis also states that as income rises, consumption will also rise but not necessarily at the same rate. That means incomeconsumption relationship is not proportional.
2.2 Normal income theories of consumption
The lifecycle hypothesis
Modigliani and Brumberg^{2} proposed the lifecycle hypothesis (LCH), it is opposite to what Keynesian function of consumption assumes. Unlike the Keynesian consumption theory is entirely based on the current income of the individuals while the concept of LCH assumes that all individuals consume a constant percentage of present value of their life income. The life cycle model also assumes that all individuals save while they work in order to finance consumption after they retire. The key assumption is that all individuals choose to maintain stable lifestyles. That means they keep their consumption levels approximately the same in every period instead of saving in one period to spend furiously in the next period.
According to the theory, consumption is a function of the consumer’s life expected income. Individual’s consumption can be said to depend on the available resources, the rate return on capital, the spending plan and the retirement age of individual which the plan is made. The theory makes three assumptions as follow:
1. There is no change in price level during the consumer’s life time
2. Interest rate is stable throughout the lift time of the consumer.
3. The consumer does not inherit any assets. Savings are his/her net assets.
The life cycle model can be expressed as:
C = (W + RY) / T, where W = Initial endowed wealth, R = retirement age, Y = Income, and T = Years of life remaining.
Rewriting consumption function of this consumer
C = γ1(1 / T) W + γ2(R / T) Y
The permanent income hypothesis
The permanent income hypothesis (PIH) is developed by Friedman^{3}. In its simple form, the hypothesis argues that consumption is not by current income but depends on expected average income and transitory income. The key conclusion of this theory is that transitory, shortterm changes in income have little effect on consumer spending behavior. Friedman uses permanent income as the determinant of income. He split the consumption and income into permanent and transitory components. That is
Ct=Ctp+Ctq
Yt=Ytp+Ytq
Where:
Ctp is permanent consumption, and Ct Ytp is permanent income, and Ytq is transitory income.
Permanent income refers to the amount a consumer spends on consumption while keeping his/her wealth intact. Transitory income is the differences between permanent income and the measured income. Friedman concluded that the individual will consume a constant percentage of his or her permanent income and earners with low income level have a higher marginal propensity to consume while high income earners have a higher transitory element to their income and a lower than average propensity to consume.
3 Data
Economists believe that income is a main factor of influencing consumption, and consumption is a function of demand. Although, In general, there are many factors that may influence consumption, in this study, we only discuss about the relationship between income and consumption which is known as consumption function.
So all series examined in this paper, gross national income GNI (per capita) and household final expenditure consumption (per capita) are collected from World bank national accounts data. The data is annual and spans the time period from 19902010, total are 21 years.
In this paper, we use the logarithm of Gross National income (GNI) as a proxy to represent income (y) and the logarithm of household final consumption as a proxy to represent the consumption expenditure (C).
The gross national income consists of: the personal consumption expenditures, the gross private investment, the government consumption expenditures, the net income from assets abroad (net income receipts), and the gross exports of goods and services, after deducting two components: the gross imports of goods and services, and the indirect business taxes. The GNI is similar to the gross national product (GNP), except that in measuring the GNP one does not deduct the indirect business taxes.
Household final consumption expenditure (formerly private consumption) is a transaction of the national account's use of income account representing consumer spending. It consists of the expenditure incurred by resident households on individual consumption goods and services.
4 Methodology
A lot of time series literatures suggested empirical work based on time series data assumes underlying time series is stationary, if a time series is nonstationary, the spurious results are likely to arise. So we can use stationary or first differenced variable to overcome this problem. But, the use of differenced variable eliminates the long run information from data set. And merely provides short run information. To solve such kind of problem, econometrician proposes that testing to determine whether or not longrun relationship exists among variables in the model is required.
A lot of techniques are available to test for the existence of longrun equilibrium relationships in the levels among variables. Mainly, this analysis has been based on use of cointegration techniques. The most common to use is the twostep residualbased procedure for testing the null of nocointegration EngleGranger (1987) test^{4}.
Cointegration analysis using the Engle and Granger (1987) is a singleequation method and consists of two steps. For the method to be suitable, all variables in the model have to be integrated of the same order. Assuming that both variables in our bivariate model are integrated of order one, the first step in the analysis is to estimate the longrun relationship between the variables. The longrun relationship between variables Y_{t} and X_{t} is
Y_{t }= B_{0 }+B_{1}X_{t }+e_{t}
which can be estimated with ordinary least squares. After the estimation, the residual series e_{t} is extracted and saved for further analysis. If two variables are cointegrated, there exists at least one linear combination among them that yields a stationary relation. Therefore, if the residual series e_{t} is stationary, the variables Y_{t }and X_{t} are cointegrated and if e_{t} is nonstationary, the variables are not cointegrated. The second step in the Engle Granger analysis is to test the residuals for stationarity or for the presence of a unit root.
5. Empirical analysis
Timeseries properties of the data
Before applying the cointegration and the errorcorrection methodology it is necessary to determine the order of integration of each variable, by testing whether they are stationary or they include a stochastic trend, i.e. how many times each variable needs to be differenced in order to achieve stationarity. To this end, we applied the ADF (augmented DickeyFuller, 1981^{5}) tests.
As far as the logarithms of variables are concerned, we tested the null hypothesis of nonstationarity against the alternative that the series are trendstationary.
As can be seen in the next graph, the first difference of the log (consumption) and of the log (income) do not seem to have a trend.
Graph 1 First difference of the log (consumption) and of the log (income) in Russia
Tables 1 and 2 report the results of the ADF for a second unit root and for one unit root, respectively. Comparing ADF tests statistics in table 1 with their corresponding critical values, we conclude that the hypothesis of I(2) is rejected for all the series.
Table 1 The ADF test for second unit root
Variables 
Test statistics 
Pvalue 
Cons_russia 
1,397 
0,959 
Income_russia 
0,877 
0,898 
Cons_Bul 
1,641 
0,976 
Income_bul 
1,888 
0,986 
Table 2 The ADF test for one unit root^{6}
Variables 
Test statistics 
Pvalue 
Conclusion 
Cons_russia (level) 
1,461 
0,9648 

First Diff. 
3,059 
0,0071 *** 
I (1) 
Income_russia (level) 
0,7058 
0,8677 

First Diff. 
5,010 
0,0001 *** 
I (1) 
L_Cons_Bul (level) 
1,801 
0,983 

First Diff. 
2,048 
0,0563 * 
I (1) 
L_Income_bul (level) 
1,991 
0,9894 

First Diff. 
3,448 
0,0031 *** 
I (1) 
Unitroot tests are performed both in level and first difference forms using only an intercept. ADF statistics suggested that all variables include a unit root. In contrast, their first differences appear to be stationary. Therefore, each variable in our data set is integrated of order one. They both have the same order of integration, one unit root and can be cointegrated. These findings are confirmed in the study of Chukalev^{7}. In order to employ the Engle Granger test and check if log (consumption) and log (income) are cointegrated, it is necessary to test for unit root on the residual of the regression of log (Cons) = B_{0}+ B_{1}log (Income) +e
Table 3 Cointegration test using the Engle Granger procedure
Cointegration relation 
Testing for a unit root in variables (pvalues) 
Cointegration regression OLS, using observations 19912010 (T = 20) Coefficient (pvalues) 
Testing for a unit root in residuals 
Bulgarian incomeconsumption (test without constant) 
0,853 and 0,996 respectively 
Income 0,925 (1,83e029 ***)

test statistic= 2,89429 pvalue 0,0356 
Russian incomeconsumption (test without constant) 
0,953 and 0,875 respectively 
Income 0,851 (2,40e031 ***)

test statistic: = 3,54772 pvalue 0,028

The results (Table 3) show that there are positive and significant long run relationships between GNI and consumptions for Bulgaria and Russia. The sign for GNI are consistent with many consumption theories. It states that the consumption depend on income; a rise in income increases the consumption. And from the long run results we can see that the coefficient of logY is 0,925 for Bulgaria, and 0,851 for Russia. From the theories of arguments, the marginal propensity to consume (MPC) should be greater than zero but less than one. In Bulgaria, the incomeconsumption relationship is more pronounced than in Russia. Consider the differences between the two countries in terms of income over the past 10 years (see Graph 2).
During the period 20012010 has seen a significant rise in incomes in Russia than in Bulgaria. This leads to improved living standards of consumers in Russia and consumption are significantly improved and changed.
Graph 2 Comparison of income in Bulgaria and Russia for the period 20012010
(GNI per capita, Atlas method (current US$))
6. Conclusion
The object of this study is to examine the relationship between GNI and consumptions for Bulgaria and Russia. As Bulgaria and Russia have many similar points. Hence, it is quite comparable for these two countries. Studying the relationship between income and consumption, that is consumption function. It has been introduced in many kinds of papers and studies.
We find that in both countries the income consumption relationship is in the line of theory. This study we assume that the consumption only depends on GNI, only take the time period of 19102010 to analysis the relationship between variables for Bulgaria and Russia. Actually consumption is also affected by other factors. As the limitation of the time and the countries of observation, so, hopefully we can further research on the relationship between GDP and consumption by lengthening the time period, expending or change the countries to get further answers to it or adding other factors as well to further research the consumption function.
7. References
Data Source
1. Word Bank National Accounts Data
Other references
2. Chukalev, G. 2007 “Consumption, income and wealth of the households” Agency for Economic Analysis and Forecasting, Vol. 1, p.139
3. Dickey, D.A. and Fuller, W.A., 1981. Distribution of the estimators for autoregressive time series with a unit root. Econometrica 49, 105772
4. Engle, R. F. and Granger, C. W. J. (1987). CoIntegration and ErrorCorrection: Representation, Estimation, and Testing. Econometrica, 55(2):251276
5. Friedman. Milton 1957 “A Theory of the Consumption Function” Princeton University Press
6. Keynes, J.M. (1936) The general theory of employment interest and money, New York: Harcourt, Bruce and World
7. Modigliani, Franco, and Richard H. Brumberg, 1954, “Utility analysis and the consumption function: an interpretation of crosssection data,” in Kenneth K. Kurihara, ed., Post Keynesian Economics, New Brunswick, NJ. Rutgers University Press. Pp 388–436
1 Keynes, J.M. (1936) The general theory of employment interest and money, New York: Harcourt, Bruce and World
2 Modigliani, Franco, and Richard H. Brumberg, 1954, “Utility analysis and the consumption function: an interpretation of crosssection data,” in Kenneth K. Kurihara, ed., Post Keynesian Economics, New Brunswick, NJ. Rutgers University Press. Pp 388–436
3 Friedman. Milton 1957 “A Theory of the Consumption Function” Princeton University Press
4 Engle, R. F. and Granger, C. W. J. (1987). CoIntegration and ErrorCorrection: Representation, Estimation, and Testing. Econometrica, 55(2):251276
5 Dickey, D.A. and Fuller, W.A., 1981. Distribution of the estimators for autoregressive time series with a unit root. Econometrica 49, 105772
6 All calculations in this study were performed using Gretl 1.6.5 for Windows, where parameter p can be automatically determined
7 Chukalev, G. 2007 “Consumption, income and wealth of the households” Agency for Economic Analysis and Forecasting, Vol.1, p.21