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Next: Models TC and TR Up: Regional unemployment insurance Previous: Regional UI, endogenous benefit

Calibration and comparison

There are two motivations to calibrate the models. First, it is possible to visualise and to elucidate functional relationships, which can also be derived generally. The second aim is to qualify effects, which are ambiguous in general. For these results to have a weight it is important that the assumed functional forms and parameters are plausible. On the other hand, the functions should be as simple as possible.

The following functions are assumed:


utility function $u(c)=\sqrt{c}$,
   
production function $f(n,x)=\frac{1}{a} \left(n x - \frac{1}{2} n^2\right)$,
where $a$ is a positive parameter. Both functions have the assumed properties, i.e. positive first derivatives, and negative second derivatives with respect to consumption and employment, respectively6. The cross-derivative of the production function is positive, so that infrastructure has a positive effect on the productivity of labour. The labour demand function can be obtained by partially differentiating $f(\cdot)$, and rearranging: $n=x-aw$. Both, production function and utility function, have mainly been chosen due to their simplicity.

If the indicated functions are employed, the wage rate can be calculated by insertion in equation (6):

\begin{displaymath}
w=\frac{x}{a \left(7-6 \frac{\sqrt{\beta}}{\sqrt{1-\tau}} \right)}
\end{displaymath}

and, using equation (1), labour demand is

\begin{displaymath}
n=\frac{6 x}{6+\frac{\sqrt{1-\tau}}{\sqrt{1-\tau}-\sqrt{\beta}}}.
\end{displaymath}

The exogenous parameters have the values given table 1 ($\tau$ in models BC and BR and $\beta$ in models TC and TR).

Table 1: parameter values for the calibration




parameter value parameter value
$a$ $0.6$ $M$ $1$
$\beta$ $0.57$ $\tau$ 0.05
$k$ 0.27 $x^1$ $1$
$K$ $1$ $x^2$ 0.6


To assess the effects of a regionalisation of the UI´s budget, profits and expected utilities of firms and workers from both regions have to be derived. Then, the difference between the respective values with a central and with a regional UI indicates, which of the alternatives an agent prefers. If it is positive, central UI is preferable, and vice versa.



Subsections
next up previous
Next: Models TC and TR Up: Regional unemployment insurance Previous: Regional UI, endogenous benefit
Helge Sanner: Regional Unemployment Insurance, Potsdam 2001