Section VI – Modeling lifecycle income
6.3 Examination of the unemployment rate
In addition to analyzing developments in wages across time, age and income class, the risk of unemployment must be considered when defining an income model. In the following, unemployment rates will be examined based on age, education, gender and across time.
To even begin evaluating unemployment rates, a definition must be made. Our definition is similar to the one used by Danmarks Statistik and sounds: Unemployment is defined as a Danish citizen whom are currently without work but are considered part of the workforce, hence, ready and able to take on a job (Danmarks Statistik, 2019). The workforce is then defined as the sum of unemployed and employed citizens. The definition seems reasonable for our analysis, as we are only interested in people who are part of the workforce and contribute to a pension scheme. Thus, we exclude all who are not a part of the Danish workforce. The definition requires us to assume all individuals we model will stay a part of the Danish workforce until retirement.
6.3.1 General development of the unemployment rate
In figure 17, the unemployment rate in Denmark is drawn for men, women and collectively. At first, it is evident how unemployment generally has decreased significantly in the past 40 years. In the 1980s and 1990s, unemployment rates varied between 7 % and 13 %. However, in the past 15 years, the average unemployment rate has been 3.8 % with an unemployment rate of 3.1 % in 2018.
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Figure 17: Unemployment rate by sex and total 1979-2018 (Danmarks Statistik, 2019)
Another visible trend is how unemployment is somewhat correlated with economic cycles. In the period 1980-2018, Denmark has been in a recession or had very low growth five times. In 1980-81, 1988, 1993, 2002-03 and 2008-09. If comparing the economic crises with the graph, it seems unemployment rates spike with a lag after a period with low GDP-growth. In the most recent financial crisis, 2008-09, unemployment reached an all-time low in 2008. The unemployment rate reached a new peak in 2012, four years later. Similarly, the dot com crisis in 2002-03 increased unemployment. However, the increase came one year later than the crisis itself.
When looking at the unemployment rate for men and women, the difference has converged to zero. In the 1980s, women were on average 3-percentage points more unemployed. Although in the period 2010-2018, the difference has on average been precisely zero. Thus, it must be assumed that the future gap between men and women are zero.
6.3.2 Unemployment rate across lifecycles
Another exciting variable to examine is how unemployment is dependent on age. Figure 18 sketches the unemployment rate in the period 2007-2018 with monthly observations for a given age-group.
Figure 18: Unemployment rate given age groups across time (Danmarks Statistik, 2019)
Firstly, it must be concluded how average unemployment decreases with age. Thus, the highest
unemployment rate is found for the age group 25-29, whereas the lowest is found for the population older than 60 years. When zooming in on the averages, table 17 below visualizes the exact differences.
0 5 10 15
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018
Unemployment rate, pct (1979-2018)
Total Men Women
0 2 4 6 8 10 12
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
Unemployment rate (pct) given age
All Age 25-29 Age 30-39 Age 40-49 Age 50-59 Age over 60
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Table 17: Unemployment rate deviations from the mean, age groups (authors’ calculations) (Danmarks Statistik, 2019)
From the table, it is evident how the average unemployment rate in the period 2007-2018 has been 4.75 %. In the same period, the average was only 3.09 % for the age group above 60 years. The differences are quite large, with the youngest age group having more than twice the unemployment rate. Consistently, the average unemployment rate decreases for each age group. From the
numbers, it seems age is a dependent variable on the risk of unemployment. Hence, when modeling unemployment, it could be considered to include age.
6.3.3 Unemployment rate across and education
In addition to comparing employment status and age, it is relevant to examine the relationship between unemployment and level of education. Like the previous analysis, the period 2007-2018 is examined. Figure 19 below shows the unemployment rate for individuals who has the highest education. Furthermore, the growth in real GDP and fixed investments is sketched.
Figure 19: Unemployment rate, GDP, investments by year and education (Danmarks Statistik, 2019)
What is visible is how the average unemployment rate is significantly higher for individuals with only education from elementary school than higher levels of educations. In the period, the average for elementary schools was 6.7 %, in opposition to 4.9 % and 4.6 % for individuals with vocational education and master’s degree, respectively.
Thus, there seems to be a great difference between no education and education. Although the difference between vocational and higher education is relatively small. In examining the differences between individuals with a university degree and a vocational education, such as plumber,
electrician or craftsman, it seems they develop differently in the economic cycle.
-15 -10 -5 0 5 10
0 2 4 6 8 10
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Unemployment rate, GDP & investments
Fixed investments y/y (RHS) Real GDP y/y (RHS) Vocational Education (LHS) Elementary School (LHS) Master's Degree (LHS)
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university degree. If we compare the development with real GDP growth and changes in fixed investments (a proxy for constructions), we see the unemployment rate is increasing relatively more for individuals with a lower level of education. In 2007-08, just before the financial crisis, the
unemployment rate for vocational educations was lower than for individuals with a master’s degree.
The same trend is visible in 2016 and 2017. Although, post the financial crisis fixed investments dropped 13 % in 2009 and 6 % in 2010 which increased unemployment from 2.3 % to 6.6 %.
Conclusively, it seems there is a significant difference in the unemployment rate between having no education and some education. Although, the average unemployment rate for individuals with education is low. However, the standard deviation is higher for individuals with a lower level of education than individuals with a university degree. This could be caused by the nature of the job, where jobs in construction to a higher degree are correlated with economic cycles.
6.3.4 Correlations between unemployment, wages, and stocks
As salaries and contributions are used as a variable input to estimate future wealth, it is vital to make assumptions of the correlation between wages and the stock market.
Figure 20: Unemployment rate vs. total return on MSCI World (Bloomberg, 2019) (Danmarks Statistik, 2019)
Figure 20 above sketches the annual unemployment rate (LHS) and an indexed total return of MSCI World in the period 1990-2018. One can infer that there seems to be some negative correlation between the unemployment rate and the stock market return. Although, when taking a closer look, the effect on unemployment seems to be lagged a few years. This pattern is in accordance with real observations in economic cycles. Usually, in times of crisis, businesses hesitate to reduce employee costs and might wait until profits have dropped. In the example of 2008, the unemployment rate dropped to an all-time low, although the stock market decreased by 30 %. However, in the years after, the unemployment rate more than doubled from 2% to 4.3 % in 2012.
Besides the correlation between the stock market and the unemployment rate, many labor income models also consider the relationship between labor income with the stock market. For many professions, especially within the private sector, it is common to have some income dependency on the performance of the company and the company’s stock price (Munk, 2017). However, figure 21 below does, seem to indicate that no such conclusion can be drawn. The nominal wage increase is close to constant in the range of 1 % to 6 % whereas the stock market return is highly volatile.
Zooming in on good and bad performing stock years, neither, does it seem there is a connection. On
200 400 600 800 1.000
0%
2%
4%
6%
8%
10%
12%
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018
Unemployment rate & MSCI World stocks
Unemployment Rate (LHS) MSCI World (RHS)
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Thus, it could be the case some workers have a fairly large correlation on the stock market, and others do not. An example could be the difference between public and private sector employees, where it could be assumed private sector employees have a more considerable dependency on the performance of stocks.
Figure 21: Changes in nominal wages vs. MSCI World, 1988-2017 (Danmarks Statistik, 2019) (Bloomberg, 2019)
To examine the development closer, a linear regression of the nominal and real wage increase as a function of annual returns on the MSCI World index in the period 1988-2017. The linear regression can be defined as the following equation with 𝑌𝑖 being the increase in wage and 𝑋𝑖 being the changes in the MSCI World. Mathematically speaking:
𝑌𝑖 = 𝛽0+ 𝛽1∗ 𝑋𝑖+ 𝜀𝑖 (6.2)
The regression is made in MS Excel and the four outputs shown below:
Table 18: Regression output on real wage vs. total return on MSCI World. Authors' calculations
The outputs show increases in wages has no or only a little linear dependence on the stock market. Looking at the nominal wage-increase with no lag, the explanatory power 𝑅2 is only 0.035. Introducing a 1 period lag – The increase in wage as a function of the stock market return the previous year, higher 𝑅2 is reached, although, still very low. None of the coefficients are significant on a 5 % level making why we must reject the model. Thus, all four analyses indicate no strong linear relationship between wages and stock market returns. Conclusively, the relationship must be set to zero or at least at a low level of dependence.