Econometric model of unemployment rate on the example of Japan

Among the G-7 countries, the seven richest countries in the world, Eurozone countries are suffering from high and persistent unemployment. Then, what is the situation in Japan? In the 1980s, with the highest economic growth and the lowest jobless rate among the major industrial countries, Japan was shining, claiming “Japan as Number One” or “Model Japan.” After the burst of the bubble boom in 1990, the era of “a lost decade” began, in which the growth rate was nearly zero and in some years below zero. In 1997, Japan was on the verge of a great depression. In 2002 and 2003 the labor market deteriorated further, recording the highest jobless rate after the war. How high was the worst jobless rate? It was 5.25%.

So our project aims to find reasons for the increasing unemployment rate in Japan. In order to do that we will create econometric model and find out what factors influence on unemployment rate.

So, in this article will be estimating the model, where Y t is the unemployment rate in percent of total labor force. X 1t – rate of inflation, X 2t – population, X 3t – general government net debt, X 4t – current account balance.

For analyzing and testing the model, we found out some specific data. We took annual data from 1980 to 2013 about unemployment rate, rate of inflation, population, general government net debt and current account balance in Japan.

Specification of a econometrics model

Mathematical interpretation of the model is presented below:

Y t = β 0 + β 1 X 1t + β 2 X 2t + β 3 X 3t + β 4 X 4t + u t ,

E (u t ) = 0, σ (u t ) = const

Table 1 Regression statistic s

Regression Statistics

Multiple R	0,95
R Square	0,91
Adjusted R Square	0,89
Standard Error	0,37
Observations	31

Table 2 Variance analysis

df SS MS F Significance F Regression Residual Total 4 26 30 34,38 3,55 37,93 8,59 0,14 62,92 0,000000000001 Table 3 Coeffici ents Standar d Error t Stat P-valu e Lower 95% Upper 95% Lower 95,0% Upper 95,0% Intercept Rate of inflation Population General government net -13,69 -0,20 0,14 0,03 5,91 0,06 0,05 0,003 -2,32 -3,44 2,82 8,09 0,03 0,00 2 0,01 0,00 0 -25,83 -0,32 0,04 0,02 -1,55 -0,08 0,24 0,03 -25,83 -0,32 0,04 0,02 -1,55 -0,08 0,24 0,03 debt

Current account                              0,00

balance             -0,01     0,003    -3,69    1     -0,02     0,00     -0,02     -0,004

Specification of estimated econometric model:

Y t = -13,69 – 0,20X 1t +0,14X 2t +0,03X 3t – 0,01X 4t + u t

(5,91)  (0,06)   (0,05)   (0,003)  (0,003) (0,37)

F = 62,92; F crit. = 2,74

R² = 0,91; t crit. = 2,06

Model testing

Now it needs to test the model. The calculated regression coefficients β 0 , β 1 , β 2 , β 3 , β 4 , allow us to construct the equation Y t = -13,69 – 0,20X 1t +0,14X 2t +0,03X 3t – 0,01X 4t + u t , where u t is random value.

Value of multiple coefficient of determination R² equals to 0,91. It shows that 91% of total deviation of Y t is explained by the variation of the factors X 1t , X 2t . X 3t and X 4t . Such value of R² is good, as it is close to 1. It means that the selected factors do not effect significantly our model, which confirms the correctness of the inclusion in the estimated model.

The calculated level of significance 0,000000000001<0,05 (see table 2) confirms the R2 significance. R2 is not random and quality of specification of our econometrics model is high.

To check the significance of the coefficients, it is used t-test. That is to test the inequality |t|≥t crit. , where t is the value of t-statistics (table 3). If the inequality is right, the coefficient and the regressor are considered to be significant and vice versa. t crit. = СТЬЮДРАСПОБР(0,05; 26) = 2,06, where 0,05 is the level of significance, 26 is the number of degrees of freedom, it equals to n-(m+1). All absolute values of t-statistics in table 3 are more than t crit. , therefore, all the regression coefficients are significant.

The Goldfield-Quandt test also confirms that we can use OLS – method to check the model. Random disturbance are considered to be homoscedastic if both of the following inequalities are valid:

GQ ≤ F crit.

1/GQ ≤ F crit.

In the model both inequalities are valid, so the assumption about homoscedasticity of random disturbance is adequate.

So, the econometric model of unemployment was constructed and it found out what factors influence it.

From the estimated econometric model the coefficients should be interpreted the next way:

• •       If inflation increases by 1%, the unemployment rate will decrease by

0,20%;

• •       If population increases by 1 million people, the unemployment rate

will increase by 0,14%;

• •      If general government net debt increases by 1%, the unemployment

rate will increase by 0,03%;

• •       If current account balance increases by 1 billion U.S. dollars, the

unemployment rate will decrease by 0,01%;

• So, relationship between changes in unemployment rate and above listed macroeconomics indicators can be useful to policymakers and economists. This model is of good explanatory ability and can be used for general data analysis and forecasting.