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Regional UI, endogenous benefit rate (model BR)

In model BR, the UI tax rate is uniform and exogenously determined. In contrast to model BC, the budget of the UI has to be balanced within each region by adjustments of the benefit rate. Accordingly, the regional benefit rates differ in general. The condition that workers from region 2 are indifferent between staying in region 2 and going to region 1 then reads
$\displaystyle F^{mig}$ $\textstyle =$ $\displaystyle \frac{n^1}{s}\frac{K}{M} u[(1-\tau) w^1-k] + \left( 1-\frac{n^1}{s} \frac{K}{M} \right) u(\beta^1 w^1 -k)$  
    $\displaystyle - \frac{n^2}{1-s} \frac{K}{M} u[(1-\tau) w^2]-\left(1-\frac{n^2}{1-s} \frac{K}{M} \right) u(\beta^2 w^2) =0.$ (15)

The budget constraints of the regional departments of the UI read
\begin{displaymath}
F^{UI1}=\tau n^1 - \beta^1 \left(s \frac{M}{K}-n^1 \right)=0
\end{displaymath} (16)

and
\begin{displaymath}
F^{UI2}=\tau n^2 - \beta^2 \left[ (1-s) \frac{M}{K} -n^2\right]=0.
\end{displaymath} (17)

Partial differentiation of the implicit equilibrium conditions gives the comparative-static effects of the endogenous variables on each other. The derivatives of $s$ with respect to wages and employment remain unchanged as compared to model BC, except for the definition of $u^{m1,j}$ and $u^{2,j}$. The derivatives with respect to the benefit rates read

\begin{displaymath}
\frac{\partial s}{\partial \beta^1}=\frac{\frac{1}{K} \left[...
...^{m1,u} \right) + n^2 (s)^2 \left( u^{2,e}-u^{2,u} \right)} >0
\end{displaymath}

and

\begin{displaymath}
\frac{\partial s}{\partial \beta^2}=\frac{- \frac{1}{K} \lef...
...{m1,u} \right) + n^2 (s)^2 \left( u^{2,e}-u^{2,u} \right)}<0 .
\end{displaymath}

Differentiation of the balanced budget conditions gives

$\displaystyle \frac{\partial \beta^1}{\partial s}=\frac{n^1 M \tau}{K {\left( s \frac{M}{K} - n^1 \right)}^2}<0,$ $\displaystyle \frac{\partial \beta^2}{\partial s}=\frac{n^2 M \tau}{K {\left[ (1-s) \frac{M}{K} - n^2 \right]}^2}>0, $
   
$\displaystyle \frac{\partial \beta^1}{\partial n^1}=\frac{s M \tau}{K {\left( s \frac{M}{K} - n^1 \right)}^2}>0,$ $\displaystyle \frac{\partial \beta^2}{\partial n^2}=\frac{(1-s) M \tau}{K {\left[ (1-s) \frac{M}{K} - n^2 \right]}^2}>0. $
The interplay of the endogenous variables is summarised in figure 4. As in the section with endogenous tax rate, the ambiguity of some effects disappears when a regional UI is considered. The reason is that, for instance, in the model with central UI, immigration in region 1 has a negative effect on the UI´s budget because the number of unemployed in region 1 increases, and it has a positive effect because the number of unemployed in region 2 shrinks. Consequently, the total effect is not clear without additional assumptions. In the cases of regional UI, the effect is split into two unambiguous effects.
Figure 4: Partial effects in model BR
\begin{figure}\begin{center}
\special{em:linewidth 0.4pt}
\unitlength 1.00mm\l...
...e{3}} \put(62.5,20){\makebox(0,0){$+$}}
%
\end{picture}
\end{center}\end{figure}


next up previous
Next: Calibration and comparison Up: Endogenous benefit rate Previous: Central UI, endogenous benefit
Helge Sanner: Regional Unemployment Insurance, Potsdam 2001