Relationship between Stocks and Unemployment

Short link: http://wp.me/p7ciWq-1H

This paper is an ongoing research into the relationship between the level of unemployment and the level of stocks, in other words, between the unemployment rate and the stock index. It may be modified over time with the findings.

I’m beginning with a focus on data available concerning France.

France is an interesting case, as this country is experiencing some degree of deregulation in labour laws and habits, from less to more liberalism. One of the consequence is to increase the unemployment, since terminating labour contracts is facilitated by a more accommodative regulation. On the other side – the side of stock markets – the huge influx of liquidities generated by the requirement to rescue a depressed economy resulting from a shift towards more restrictive budgetary policies – a consequence of the worldwide spread of the liberal argument that a better functioning of the economy requires reducing the size of state intervention – results in stimulating stocks, hence reducing dividends to prices ratios, hence inciting companies to cut labour costs.

However, the preliminary findings show an inverted relationship, with a lag of about one year (12 months), i.e. the unemployement rate falls about a year after a stock market rise.

Data

Country : France
Data sources : DARES (unemployment)
INSEE (activity and population)
Working days calendar
Data are monthly
Period covered : January 1996 to September 2015

Variables

RFE : Unemployment rate (%)
CAC40 : France Stock Market Index
jo : working days in France (around 21)
DATEMONTH : time index in form YYYY.(M/12)

Analysis

Multiple Regression – LOG(RFE)
Dependent variable: LOG(RFE)
Independent variables:
LOG(LAG(jo,1))
LOG(LAG(CAC40,15))
LOG(DATEMONTH)

Standard T
Parameter                          Estimate       Error           Statistic      P-Value
CONSTANT                      -82.4664      21.3816       -3.85689    0.0002
LOG(LAG(CAC40,15))   -0.354393       0.02704 -13.1062       0.0000
LOG(DATEMONTH)       11.4289           2.81522     4.05968    0.0001

Analysis of Variance
Source              Sum of Squares Df  Mean Square F-Ratio P-Value
Model              1.90852                2   0.954258          89.11    0.0000
Residual           2.23826               209                       0.0107094
Total (Corr.) 4.14677 211

R-squared = 46.0241 percent
R-squared (adjusted for d.f.) = 45.5076 percent
Standard Error of Est. = 0.103486
Mean absolute error = 0.0817462
Durbin-Watson statistic = 0.121789 (P=0.0000)
Lag 1 residual autocorrelation = 0.919605

Stepwise regression
Method: forward selection
P-to-enter: 0.05
P-to-remove: 0.05

Step 0:
0 variables in the model. 211 d.f. for error.
R-squared = 0.00% Adjusted R-squared = 0.00% MSE = 0.0196529

Step 1:
Adding variable LOG(LAG(CAC40,15)) with P-to-enter =0
1 variables in the model. 210 d.f. for error.
R-squared = 41.77% Adjusted R-squared = 41.49% MSE = 0.0114988

Step 2:
Adding variable LOG(DATEMONTH) with P-to-enter =0.0000696167
2 variables in the model. 209 d.f. for error.
R-squared = 46.02% Adjusted R-squared = 45.51% MSE = 0.0107094

Final model selected.

Output

The output shows the results of fitting a multiple linear regression model to describe the relationship between LOG(RFE) and 3 independent variables. The equation of the fitted model is

LOG(RFE) = -82.4664 – 0.354393*LOG(LAG(CAC40,15)) + 11.4289*LOG(DATEMONTH)

Since the P-value in the ANOVA table is less than 0.05, there is a statistically significant relationship between the variables at the 95.0% confidence level.

The R-Squared statistic indicates that the model as fitted explains 46.0241% of the variability in LOG(RFE).

The adjusted R-squared statistic is 45.5076%. The standard error of the estimate shows the standard deviation of the residuals to be 0.103486.

The mean absolute error (MAE) of 0.0817462 is the average value of the residuals.

The Durbin-Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in the data. Since the P-value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level.

The highest P-value on the independent variables is 0.0001, belonging to LOG(DATEMONTH). Since the P-value is less than 0.05, that term is statistically significant at the 95.0% confidence level.

Charts

Crosscorrelation RFE with CAC 20151115

LOG(RFE) 20150915Residal plot on predicted LOG(RFE) 20151115

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