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Models TC and TR

Figure 5 shows the preferences of firms and workers concerning the organisation of UI for different benefit rates. Positive values mean that the expected utility or the profits are higher with a central UI, negative values mean that regional UI is prefered. The definitions and interpretations of the curves are:
$\displaystyle Fi\equiv$ $\textstyle \pi^i_{TC}-\pi^i_{TR}$ $\displaystyle \left\{ \begin{array}{cl}
>0 & \parbox{8cm}{firms from region i p...
... & \parbox{8cm}{firms from region i prefer regional UI} \\
\end{array} \right.$  
      (18)
$\displaystyle Wi\equiv$ $\textstyle Eu^i_{TC}-Eu^i_{TR}$ $\displaystyle \left\{ \begin{array}{cl}
>0 & \parbox{8cm}{workers from region i...
... \parbox{8cm}{workers from region i prefer regional UI} \\
\end{array} \right.$  

Apart from the preferences of the agents, an efficiency criterion, $z$, is used to assess the reform. For this aim the total production in both regions have to be calculated, lowered by the total costs of migration. Related to one firm from each region, the variable is defined as follows:

\begin{displaymath}
z \equiv f(n^1,x^1)+f(n^2,x^2)-k \left(m^1-\frac{M}{2K}\right) .
\end{displaymath}

The number of workers per firm is $M/2K$ ex ante since workers are distributed evenly across all firms (see assumption A4). To find out under which arrangement more income rests for consumption, the difference between $z$ in the case of central UI and $z$ in the case of regional UI is calculated:
$\displaystyle \Delta z = z_{TC}-z_{TR}$ $\textstyle =$ $\displaystyle f_{TC}(n^1,x^1)+f_{TC}(n^2,x^2)$ (19)
    $\displaystyle - \left[ f_{TR}(n^1,x^1)+f_{TR}(n^2,x^2) \right] -k \left(m_{TC}^1-m^1_{TR}\right).$  

Again, positive values signify an advantage of central UI and negative ones that regional UI is preferable. If, for instance, the value of $\Delta z$ is positiv, it is potentially possible that all workers and firms are better off with central UI if the excess of production is distributed appropriately.

In contrast to the above mentioned intuition, figure 5 shows, that central UI may well be preferable for efficiency reasons. For every given benefit rate $\beta$, $\Delta z$ is positiv. This means, that firms and workers who profit from central UI, could compensate those, who are worse off. The figure also shows, that only firms from the rich region would be better off with regional UI. With the given functional relationships and parameters, the conjecture that the interests of agents from the poor region are contrary to the interests of those from the rich region, cannot be confirmed. While the profit differences for the firms are considerable, the preferences of workers from both regions toward central UI are only weak.

Figure 5: Preferences and efficiency with endogenous tax rate

\fbox{
\includegraphics*[2cm,1.9cm][13.1cm,10.1cm]{tctr.eps}}

The described results can be explained by the partial effects summarised in figures 1 and 2. Because region 1 (region 2) has an unemployment rate below (above) average, the UI tax rate is lower (higher) in the case of regional UI. If workers are sufficiently risk-averse, this leads to lower (higher) equilibrium wages. Then, employment is higher (lower) in equilibrium, which reinforces the initial effect on the UI tax rate. The effects on the expected utility of workers and also on migration are not quite clear, yet. On the one hand, the relatively lower UI tax rate and higher probability of entering employment have a positive impact on migration from the poor to the rich region, respectively. On the other hand, wages are, in comparison to central UI, higher in the poor region, and lower in the rich region, which has a negative influence on migration. For the specific functions and parameter values we assume the positive effect prevails, so that equilibrium migration is higher in the case of regional UI. The additional costs of migration may explain to some extent, why the efficiency criterion supports central UI. The contrary effects on the expected utilities, together with compensatory migration involve the relatively small preference of workers from both regions towards central UI.


next up previous
Next: Models BC and BR Up: Calibration and comparison Previous: Calibration and comparison
Helge Sanner: Regional Unemployment Insurance, Potsdam 2001