Acta Universitatis Danubius. Œconomica, Vol 14, No 4 (2018)

Correlation between Total Unemployment and Expenses with Unemployed Social Protection in Romania

Gabriela – Mariana Ionescu¹

Abstract: The goal of the study is to estimate the correlation between two important macroeconomic variables in the labour market: the total unemployment rate over the active population (as dependent variable), respectively the rate of social protection expenditures with the unemployment over GDP (as independent or causal variable) in Romania. In order to achieve the goal, the following objectives were achieved: a) the formation of time series and the statistical analysis for the two variables; b) designing a mono-factorial linear econometric model; c) estimation of the econometric model. The empirical data used are quarterly data between January 1997 and December 2016. The data quality was provided by using the following sources: EUROSTAT, respectively the Romanian Statistical Yearbook. The main scientific results of the study are as follows: 1) statistically the time series of the two variables are stationary only at the level of the first order differences, the series of the independent variable is non-normal, and the dependent variable is quasi-normal; 2) the estimation of the quantitative model shows that there is a direct correlation (though weak, about 3%) between the dependent and the independent variable. At the same time, there are no influences outside the independent variable (the free term of the first degree equation is approximately - 0.002). In conclusion, it can be said that the variation of the total unemployment rate in the active population is direct, albeit relatively weak, influenced by the change in the rate of social protection expenditures in GDP.

Keywords: unemployment total rate; social protection expenditures; stationarity; first order differences; seasonality.

JEL Classification: C10; J64; O11

1. Introduction

To achieve the goal of the study two macroeconomic variables which are working on the labour market are taken into consideration, namely: a) the total unemployment rate over the active population (as dependent variable); b) the rate of social protection expenditures with the unemployment over GDP (as independent or causal variable) in Romania.

The correlation analysis between the two variables analysed in this paper considers two aspects. Firstly, the unemployed existence (those registered at the National Agency for Employment of Romania) directly leads to the social protection costs formation of the unemployed. Carrying out these costs has the effect (at least an in intention or expectation) or reducing unemployment (Mankiw, 2015), for example by finding jobs as a result of retraining funded by these costs.

Secondly, the unemployment benefit, as a component of social protection expenditure for the unemployed, may encourage the unemployment maintenance (by creating moral hazard). Therefore, it is obvious that the two variables are correlated.

The independent variable of the mono-factorial linear regression model, the rate of the social protection expenditure for the unemployment refers to the total expenditure related to the unemployment, calculated as ratio between social protection costs of the unemployment and GDP.

The dependent variable of the mono-factorial regression model, thus the unemployment rate refers to the total unemployment (both short and long term), calculated as ratio between unemployed number and active population. The data series includes quarterly registration expressed as a percentage (data source being EUROSTAT).

2. The Topic Importance/Relevance

The economic product distribution in society is a fundamental issue, and also a questionable problem of economic discourse, both in the conceptual and methodological aspect (Dinga, E., 2011), and under the social policy too. The common research does not visit this issue from the perspective of the correlation between the total rate of unemployment over active population on the one hand, and the rate of social protection expenditures over GDP. However, it is possible that the unemployment benefits exert a behavioural impact on the kinematics of the total rate of unemployment. In such a context, the study is aimed at to examine a possible correlation (maybe even a possible causality) between the evoked variables.

2. Short Statistical Analysis of the Time Series

The (kinematic) evolution of the two variables, the independent variable , and the dependent variable , for the analysed period shows that, in the case of the independent variable , the quarterly values of social protection expenditure for the unemployed, as a GDP share, has a long-term downward trend. At the same time, there is a strong oscillation on the medium and short term. This oscillation can be interpreted either as a result of the change in the unemployment rate, or as an effect of budgetary policy decisions.

The quarterly values of the unemployment rate (Statistical yearbook of Roumania, 2017), as a share of the number of unemployed people over the active population, exhibit two behaviour patterns: a) permanent increases (although there are short-term oscillators) on the 1997 – 2002 period, respectively between 2008 – 2013; b) permanent decreases (although there are short-term oscillators) on the 2002 – 2008 period, respectively between 2013 – 2016. On 2008 there is an extremely sharp reduction in the unemployment rate, the result of substantial economic growth of that year (starting next year, with the international financial crisis in Romania, unemployment is rising).

From the perspective of the simultaneous evolution of the two variables, it can be noticed that on the 1997 – 2002 period the two variables evolve in a contradictory way (while the unemployment rate is steadily rising, the social expenditure rate with the unemployment protection decreases, except for the beginning of the period, where increases and decreases alternate). Starting with 2012, both variables decrease almost concerted as shown in figure 1.

Figure 1. Simultaneous kinematics of the two variables

Source: author’s work

Stationary analysis for the independent variable , for observed values (level values), was done using the correlogram, and Dickey-Fuller test (Books, C., 2014). From the correlogram graph (which is decreasing depending on the number of lags considered), as shown in figure 2a, can be concluded that the series of the independent variable at the observed values (level values) is non-stationary. In order to check rigorously the stationary/non-stationary character of the series, the unit root test was done. It can be observed (figure 2b), that the calculated value of the test (-3.001) is greater than the tabulated values for all three levels of significance (1%: - 4.09; 5%: - 3.47; 10%: - 3.16).

Consequently, the time series of the independent variable for the observed values (level values) is non-stationary (the null hypothesis is accepted).

Figure 2. The correlogram and Dickey – Fuller test for the independent variable X – registered values

Source: author’s work

The stationarity of the independent variable was then analysed as first-order differences of the level values . From the correlogram graph (which is relatively constant depending on the number of lags considered), we can conclude that the time series of the independent variable is stationary (figure 3a). In order to check rigorously the stationary/non-stationary character of the series the unit root test was done. It can be observed from figure 3b that the calculated value of the test (-3.48) is greater than the tabulated value for the significance level 1%: - 4.08, but is lower that the tabulated value for the significance level 5%: - 3.47, as well as the tabulated value for the significance level 10%: - 3.16. Consequently, the time series of the independent variable is stationary (the null hypothesis is rejected) only for significance levels equal or greater than 5%.

Figure 3. The correlogram and Dickey – Fuller test for the independent variable – first-order differences

Source: author’s work

The analysis of the dependent variable stationarity, for observed values (level values), as shown in figure 4a and the correlogram graph (which is, at the same time, decreasing but also oscillating depending on the number of lags considered) shows that the series of the dependent variable at the level of observed values (level values) is non-stationary. To verify rigorously the stationary/non-stationary character of the series, the unit root test was done.

As seen in figure 4b, the calculated value of the test (-2.57) is greater than the tabulated values for all three levels of significance (1%: - 4.08; 5%: - 3.47; 10%: - 3.16). Consequently, the time series of the dependent variable Y for the observed values (level values) is non-stationary (the null hypothesis is accepted).

In this case, the time series stationarity will be checked in the case of quarterly values calculated as first-order differences of the level values.

Figure 4. The correlogram and Dickey – Fuller test for the dependent variable – registered values

Source: author’s work

The dependent variable stationarity is highlighted by the correlogram graph (which is relatively constant depending on the number of lags considered) as seen in figure 5a, so the series of the dependent variable is stationary. In order to check rigorously the stationary/non-stationary character of the series the unit root test was done.

The Dickey – Fuller test data shows that the calculated value of the test (-6.12) is lower than the tabulated values for all three levels of significance 1%: - 4.08; 5% - 3.47; 10% - 3.16. Consequently, the time series of the variable is stationary (the null hypothesis is rejected) for any of the levels of tabulated significance.

Figure 5. The correlogram and Dickey – Fuller test for the dependent variable – first-order differences

Source: author’s work

The paper presents the statistical analysis of the two-stationary series, and . As seen in figure 6, the histogram of the independent variable shows that the series does not have a normal distribution, the average of the share of the rate of social protection expenditure of the unemployed over GDP is -0.08% during the whole period. As for the statistical distribution of the series, of the Skewness indicator value, i.e. the asymmetry coefficient (1.71) it is found that it is not a normal distribution. As for the value of the indicator showing the flattening of the distribution (Kurtosis: 7.46) the value greater than 3 indicates a leptokurtotic distribution. The value of the Jarque–Bera test is 103.91 (which indicates, by comparing the difference between the asymmetry coefficient and the flattening coefficient against the normal distribution, the degree of normality of the distribution) has a null probability associated, so the hypothesis of the normal distribution of the time series is rejected.

Figure 6. The histogram and the quantiles graph for the variable

Source: author’s work

The statistical analysis of the dependent variable , as seen in figure 7a shows that the average of the total unemployment rate series over the active population is -0.005% during the whole period. As for the statistical distribution of the series, of the Skewness indicator value, i.e. the asymmetry coefficient (0.27) it is observed that it is a relatively close distribution of the normal distribution. As for the value of the indicator which shows the flattening of the distribution (Kurtosis: 4.22) the value greater than 3 indicates a leptokurtotic distribution. The value of the Jarque–Bera test: 4.96, has a very low probability associated, so the hypothesis of the normal distribution of time series is rejected.

The quantiles graph of the dependent variable (figure 7b) reveals an overlap of the distribution of the residual quantiles with the normal distribution.

Figure 7. The histogram and the quantiles graph for the variable

Source: author’s work

It is observed that the quarterly averages of the independent variable differ significantly among them, which indicates a strong seasonality of social protection expenditure for the unemployed as seen in figure 8. The same phenomenon has also been encountered in the analysis of seasonality on observed values (level values) which means that the seasonality attribute of this time series has more deeper causes than those involved in the statistical calculation.

Figure 8. Seasonality of the time series D(X), together with the quarterly average indication

Source: author’s work

The quarterly averages of the dependent variable , as seen in figure 9, differ very little among them, keeping close the same value, which indicates an absence of seasonality over the unemployment rate. The same phenomenon has also been encountered in the analysis of seasonality on observed values (level values) which means that the seasonality attribute is not proper to this time series.

Figure 9. Seasonality of the time series , together with the quarterly average indication

Source: author’s work

The long-term trend (the Hodrick – Prescott trend) for the two variables analysed in the current paper, respectively the independent variable , the rate of social protection expenditure of the unemployed over GDP, and the dependent variable , the total unemployment rate over the active population as seen in figure 10, and figure 11 show the evolution of the two-time series in relation to the time axis.

By eliminating the cyclicality (seasonality) variation of the independent variable , using the Hodrick – Prescott filter, there is a flat de-seasoned trend (zero slope in relation to the time axis), during the analysed period, having linear type pattern.

Figure 10. The long-term trend of the expenditure rate change with the unemployed social protection

Source: author’s work

By eliminating the cyclicality (seasonality) variation of the dependent variable , using the Hodrick – Prescott filter, there is a much more flattened deseasonalized trend than in the case of recorded values (level values), during the analysed period, having a quasi-sinusoidal pattern.

Figure 11. The long-term trend of the unemployment rate variation

Source: author’s work

2. A Mono-Factorial Linear Regression Model

The linearity property of the correlation between the two variables involved in the study is suggested by the „points cloud” showed in the figure 12:

Figure 12. The „points cloud” of the variables involved

Source: author’s work

By approximation:

By eliminating of the variable between the two equations, gives the following equation relating and :

So, a linear relation between the dependent variable y and the independent variable x is considered:

where , respectively .

Parameters estimation:

Figure 13. The estimation of the econometric model parameters

Source: author’s work

Final equation:

The hypothesis verification of the linear regression model show that the average of errors is null : - 0.000000000000000913, as seen in figure 14 of the histogram graph.

Figure 14. The histogram of the linear regression model errors

Source: author’s work

The errors are linearly dependent on each other and are positively correlated , error spreading is constant and finite (homoscedasticity property), there are no correlations between the residual and the independent variable , and the series of errors is normally distributed .

Figure 15. Correlations between the residual and the independent variable

Source: author’s work

The confidence intervals for estimated coefficients were determined, as seen in figure 16, and the ellipse of the confidence intervals of the estimated values for the regression equation coefficients is presented in figure 17.

5. Conclusions

Regarding the first objective of the study (the formation of time series and the statistical analysis for the two variables), the time series of the two variables are stationary only for the first-order differences (in the case of the independent variable, for significance levels ≥ 5%), for the statistical distribution of the independent variable the econometric model has highlighted the fact that there is no normal distribution, while the statistical distribution of the dependent variable is near normal. The analysis of seasonality showed that the independent variable is strongly seasonalized (as a result of quarterly GDP seasonality), while the dependent variable does not show seasonality at the level of quarters, thus the trend of the independent variable is almost horizontal, while the dependent variable exhibits a weak sinusoidal trend (much more flattened than the constant trend to level values). Regarding the second objective of the study (designing a mono-factorial linear econometric model), we have found (by „points cloud” of the two data series) that two series of data are linearly correlated by means of a mono-factorial linear regression model. So, we could establish an econometric mono-factorial model. Regarding the third objective of the study (estimation of the econometric model), we have obtainted a direct proportional relationship between the dependent variable and the independent one as follows: , where , respectively .

The main scientific results of the study are as follows: 1) statistically the time series of the two variables are stationary only at the level of the first order differences, the series of the independent variable is non-normal, and the dependent variable is quasi-normal; 2) the estimation of the quantitative model shows that there is a direct correlation (though weak, about 3%) between the dependent and the independent variable. At the same time, there are no influences outside the independent variable (the free term of the first degree equation is approximately - 0.002). In conclusion, it can be said that the variation of the total unemployment rate in the active population is direct, albeit relatively weak, influenced by the change in the rate of social protection expenditures in GDP.

6. References

Dinga, E. (2011). Economics II. Macroeconomics, Cours notes, pp. 111 – 113.

Jula, D. & Jula, N. (2017). Economic modeling. Econometric and optimization models. Bucharest: The Publishing house Mustang.

Brooks, C. (2014). Introductory Econometrics for Finance, 3 rd Edition, Cambridge University Press;

Mankiw, G. (2015). Principles of Economics. Cengage Learning.

***EUROSTAT. Web page. Retrieved from http://ec.europa.eu/eurostat/data/database. Date: 02.06.2017.

***STATISTICAL YEARBOOK OF ROMANIA. Web page. Retrieved from www.insse.ro/cms/ro/tags/anuarul-statistic-al-romaniei, date 02.06.2017.

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