Definitions of variables based on the German System of National Accounts - click here.

Definitions of the theoretical variables:

For the nominal wage rates (wr) we use the monthly labour costs per employee:

wr = lkmo

The seasonal adjustment (smoothing) is achieved by the definition of the wage rate change (wr_ch) based on a four quarter difference:

wr_ch = (wr - wr(-4))/wr(-4)*100

The unemployment rate (ue) and its moving average (ue_ma) of four quarters is based on the number of unemployed divided by the workforce (in percetage points) reported by the Statistisches Bundesamt:

series ue = ewlosprz

ue_ma = @movav(ue,4)

As indicator for the inflation we utilise the chained consumer price index and, accordingly, the one of the import prices (Pim), and of the export prices (Pex).

infl = (cpripe-cpripe(-4))/cpripe(-4)*100

impe_ch = (impe - impe(-4))/impe(-4)*100

expe_ch= (expe - expe(-4))/expe(-4)*100

The values for the productivity equal the labour productivity per employee.

apew_ch =(apewki-apewki(-4))/apewki(-4)*100

The profit rates (R) are operationalized by property income related to the income of employees.

r = (yuv - yan/ewan*ewslb)/yan*100

r_ch = (r-r(-4))/r(-4)*100

The State Space Model:

Abbreviations:

c = a constant unequal to zero in the state equation, simulating a trend
w = state equation without a constant, c set to zero
f = fluctuating
s = smooth
var(e1) = Variance of the error term in signal equation
var(e2) = Variance of the error term in state equation

Definition of the four different models:

Model cs: var(e1) = 1, var(e2) = 0.001, c = free
Model cf: var(e1) = 1, var(e2) = 0.1, c = free
Model ws: var(e1) = 1, var(e2) = 0.033, c=0
Model wf: var(e1) = 1, var(e2) = 1,c=0

Common parameters of all four models:

Sample: 1973q1 2010q2
Start value = 0.666429

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