next up previous
Next: Regional UI, endogenous benefit Up: Endogenous benefit rate Previous: Endogenous benefit rate

Central UI, endogenous benefit rate (model BC)

In the case of a central UI, the conditions for a migration equilibrium and for a balance budget remain, compared to model TC, formally unchanged. The only difference is, that $\beta$ is endogenous, while $\tau$ is given. The conditions read
$\displaystyle F^{mig}$ $\textstyle =$ $\displaystyle \frac{n^1}{s}\frac{K}{M} u[(1-\tau) w^1-k] +\left(1-\frac{n^1}{s} \frac{K}{M} \right) u(\beta w^1 -k)$  
    $\displaystyle - \frac{n^2}{1-s} \frac{K}{M} u[(1-\tau) w^2]-\left(1-\frac{n^2}{1-s} \frac{K}{M} \right) u(\beta w^2) =0$ (13)

and
\begin{displaymath}
F^{UI}= n^1 K \tau w^1 + n^2 K \tau w^2- (s M-n^1 K) \beta w^1- [(1-s) M - n^2 K] \beta w^2 =0.
\end{displaymath} (14)

Partially differentiating equations (13) and (14) gives

$ \displaystyle \frac{\partial \beta}{\partial n^1}=\frac{K w^1 \beta (\tau + \beta)}{E}>0$ $\displaystyle \frac{\partial \beta}{\partial n^2}=\frac{K w^2 \beta (\tau + \beta)}{E}<0$
   
$\displaystyle \frac{\partial \beta}{\partial w^1}=\frac{\beta \left( K n^1 (\beta + \tau ) - \beta s M \right)}{E}>0$ $\displaystyle \frac{\partial \beta}{\partial w^2} = \frac{\beta \left( K n^2 (\beta + \tau ) - \beta (1-s) M \right)}{E}<0$
   
$\displaystyle \frac{\partial \beta}{\partial s}= \frac{- (\beta )^2 M (w^1-w^2)}{E}<0$
and

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

In contrast to the derivatives of $\tau$ in model TC, the derivatives of $\beta$ have the inverse sign because the impact of an increase of the benefit rate on the balance of the UI has the same direction as the impact of a decrease of the tax rate. This means, that the signs of the derivatives with respect to wages require that the rate of employment in region 1 is higher than in region 2 (condition a, see the appendix). $\partial \beta/\partial s$ has the indicated sign if condition b is met. UI benefits have an ambiguous effect on migration in general. It is negative, if the following inequality holds (condition d):

\begin{displaymath}
(1-s) w^1 \left( s M - n^1 K \right) u_c^{m1,u} < s w^2 \left( (1-s) M - n^2 K \right) u_c^{2,u}.
\end{displaymath}

Model BC consists of equations (1) and (6) respectively for both regions, equations (13) and (14). Figure 3 illustrates the interplay of the endogenous variables. Again, the ambiguous effects are labeled with the letter of the condition that must be fulfilled.
Figure 3: Partial effects in model BC
\begin{figure}\begin{center}
\special{em:linewidth 0.4pt}
\unitlength 1.00mm\l...
...}} \put(111.5,32.5){\makebox(0,0){$-$}}
%
\end{picture}
\end{center}\end{figure}


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