Structural differences across macroregions: an empirical investigation

Abstract

Using a macro–micro econometric framework that allows studying the labour market dynamics, this paper offers an in-depth investigation of the structures of both national and macro regional labour markets in Italy. The simulation results reveal structural differences between regions in the short as well as the long run. Regional gaps represent one of the main components of the natural unemployment rate in Italy. The results may help regional and national policy makers in the European Union to formulate strategies tailored to the specific needs of regional labour markets.

Appendix: Variables and equations

See Table 5.

Table 5 List of variables

1.1 Macro block

1.1.1 Stochastic equations

$$\begin{aligned} \Delta \log (EEIND)_{i,t} &= c_i(1)+c_i(2)\Delta \log (EEIND)_{i,t-1}+c_i(3)\Delta \log (VAIND)_{i,t} \\&\quad+\,c_i(4)\Delta \log (WIND)_{i,t}+c_i(5)\log (EEIND)_{i,t-1} \\&\quad+\,c_i(6)\log (VAIND)_{i,t-1}+c_i(7)\log (WIND)_{i,t-1}+\varepsilon _{i,t} \end{aligned}$$

(7.1)

$$\begin{aligned} \Delta \log (EESER)_{i,t}&= {} c_i(8)+c_i(9)\Delta \log (EESER)_{i,t-1}+c_i(10)\Delta \log (VASER)_{i,t} \\&\quad+\,c_i(11)\Delta \log (WSER)_{i,t}+c_i(12)\log (EESER)_{i,t-1} \\&\quad+\,c_i(13)\log (VASER)_{i,t-1}+c_i(14)\log (WSER)_{i,t-1}+\nu _{i,t} \end{aligned}$$

(7.2)

$$\begin{aligned} \Delta \log (PR)_{i,t}&= {} c_i(15)+c_i(16)\Delta \log (PR)_{i,t-1}+c_i(17)\Delta \log (SERATE)_{i,t} \\&\quad+\,c_i(18)\Delta \log (EERATE)_{i,t}+c_i(19)\Delta \log (IMMIG)_{i,t}+c_i(20)\log (PR)_{i,t-1} \\&\quad+\,c_i(21)\log (SERATE)_{i,t-1}+c_i(22)\log (EERATE)_{i,t-1}+c_i(23)\log (IMMIG)_{i,t-1}+\zeta _{i,t} \end{aligned}$$

(7.3)

$$\begin{aligned} \Delta \log (SE)_{i,t}&= {} c_i(15)+c_i(16)\Delta \log (SE)_{i,t-1}+c_i(17)\Delta \log (PROFSE)_{i,t} \\&\quad+\,c_i(18)\Delta \log (YUR)_{i,t}+c_i(20)\log (SE)_{i,t-1} \\&\quad+\,c_i(21)\log (PROFSE)_{i,t-1}+c_i(22)\log (YUR)_{i,t-1}+\xi _{i,t} \end{aligned}$$

(7.4)

1.1.2 Identities

$$TE_{i,t}= {} EEIND_{i,t} + EESER_{i,t} + EEOTH_{i,t} + SE_{i,t}$$

(7.5)

$$TEI_{i,t}= {} \gamma TE_{i,t}$$

(7.6)

$$LF_{i,t}= {} PR_{i,t} * POP_{i,t}$$

(7.7)

$$UR_{i,t} = {} \frac{LF_{i,t}-TEI_{i,t}}{LF_{i,t}}*100$$

(7.8)

$$\begin{aligned} PROFSE_{i,t}=\frac{PROF_{i,t}}{SE_{i,t}} \end{aligned}$$

(7.9)

1.2 Micro block

$$\begin{aligned} pne_{i,t}&= {} \frac{ne_{i,t}}{ne_{i,t}+nu_{i,t}} \end{aligned}$$

(7.10)

$$\begin{aligned} ue_{i,t}U + ne_{i,t}N&= {} (eu_{i,t} + en_{i,t})E \end{aligned}$$

(7.11)

$$\begin{aligned} eu_{i,t}E + nu_{i,t}N&= {} (ue_{i,t} + un_{i,t})U \end{aligned}$$

(7.12)

$$\begin{aligned} N&= {} \frac{(eu_{i,t} + en_{i,t})}{ne_{i,t}E}- \frac{ue_{i,t}}{ne_{i,t}U} \end{aligned}$$

(7.13)

$$\begin{aligned} N&= {} \frac{-eu_{i,t}}{nu_{i,t}E}- \frac{(ue_{i,t}+un_{i,t})}{nu_{i,t}U} \end{aligned}$$

(7.14)

$$\begin{aligned} e_{i,t}E&= {} d_{i,t}U \end{aligned}$$

(7.15)

$$\begin{aligned} e_{i,t} &= {} eu_{i,t}+(1-pne_{i,t})*en_{i,t} \end{aligned}$$

(7.16)

$$\begin{aligned} USS_{i,t}&= {} \frac{e_{i,t}}{e_{i,t}+ue_{i,t}+un_{i,t}*pne_{i,t}}*100 \end{aligned}$$

(7.17)

$$\begin{aligned} DIFFUR_{i,t}&= {} UR_{i,t} - USS_{i,t} \end{aligned}$$

(7.18)

$$\begin{aligned} num\_ue_{i,t}&= {} \exp \left( \alpha ^{[ue]}_{i,t} + \beta ^{[ue]}_{i,t} UR_{i,t}\right) \end{aligned}$$

(7.19)

$$\begin{aligned} num\_un_{i,t}&= {} \exp \left( \alpha ^{[un]}_{i,t} + \beta ^{[un]}_{i,t} UR_{i,t}\right) \end{aligned}$$

(7.20)

$$\begin{aligned} ue_{i,t}&= {} \frac{num\_ue_{i,t}}{num\_ue_{i,t}+num\_un_{i,t}+1} \end{aligned}$$

(7.21)

$$\begin{aligned} un_{i,t}&= {} \frac{num\_un_{i,t}}{num\_ue_{i,t}+num\_un_{i,t}+1} \end{aligned}$$

(7.22)

$$\begin{aligned} p_{ab, t(h)}&= {} Pr = (X_{t,h}= b|X_{t-1,h} = a,z_{t,h}) , \end{aligned}$$

(7.23)

$$\begin{aligned} P_{ab, h}&= {} \frac{\exp {z^h_t\beta _b}}{\sum ^2_{l=0}\exp {(z^h_t\beta _l)}}, \end{aligned}$$

(7.24)

1.3 Micro–macro block link

$$\begin{aligned} ab_{i,t} = \frac{exp(\alpha ^{[ab]}_{i,t} + \beta ^{[ab]}_{i,t} UR_{i,t})}{exp(\alpha ^{[ab]}_{i,t} + \beta ^{[ab]}_{i,t} UR_{i,t}) + exp(\alpha ^{[ac]}_{i,t} + \beta ^{[ac]}_{i,t} UR_{i,t}) + 1} \end{aligned}$$

(7.25)

where $i={\textit{Italy, North, Centre, South}}$ and $t=1970,1971,\dots ,2010$.