Earnings mobility among Italian low-paid workers

Abstract

This paper uses Italian panel data to analyse low pay transitions since the early 1990s. Results indicate that having more human capital reduces the probability of falling into low pay, but there is little impact on raising exit rates from low pay. Human capital effects are found to be larger for women than for men. There is considerable state dependence: the experience of low pay raises the probability of subsequent low pay episodes. Also, there is substantial unobserved heterogeneity associated with factors such as initial conditions, mobility out of the earnings distribution and educational attainment.

Appendix

The model of Section 3 is a four-variate probit with endogenous truncation and endogenous switching. The four equations, given in the text, are:

$$l^{ * }_{{it - 2}} = \beta ^{\prime } x_{{it - 2}} + u_{{it - 2}} ,u_{{it - 2}} \, \sim \,N{\left( {0,1} \right)},{\kern 1pt} \,L_{{it - 2}} = I{\left( {l^{ * }_{{it - 2}} > 0} \right)}\quad \quad \quad \quad \;{\text{Initial conditions}}$$

(7)

$$ r^{ * }_{{it - 2}} = \psi ^{\prime } w_{{it - 2}} + \varepsilon _{{it}} ,\varepsilon _{{it}} \sim N{\left( {0,1} \right)},R_{{it}} = {\text{I}}{\left( {^{ * }_{{it - 2}} \, > \,0} \right)}\quad {\kern 1pt} \,\quad \;\quad \quad \quad \quad {\text{Earnings retention}} $$

(8)

$$s^{ * }_{i} = {\text{ $ \theta $ }}^{\prime } h_{i} + \xi _{i} ,\xi _{i} \sim N{\left( {0,1} \right)},S_{i} = {\text{I}}{\left( {s^{ * }_{i} > 0} \right)}\quad \quad \quad \quad \quad \quad \quad \quad {\text{Educational attainment}}$$

(9)

$$l^{ * }_{{it}} = {\left[ {L_{{it - 2}} \gamma _{1} \prime + H_{{it - 2}} \gamma _{2} \prime } \right]}z_{{it - 2}} + \nu _{{it}} \;{\kern 1pt} {\kern 1pt} {\kern 1pt} {\text{if}}\;{\kern 1pt} {\kern 1pt} \,R_{{it}} = 1,\,{\kern 1pt} \,\nu _{{it}} \sim N{\left( {0,1} \right)},\,{\kern 1pt} L_{{it}} = {\text{I}}{\left( {l^{ * }_{{it}} > 0} \right)}\quad \,\quad \quad \quad {\text{Low pay transition}}$$

(10)

The low pay transition equation is truncated for observations that leave the sample between t−2 and t (i.e. when R _it =0) and allows switching of the parameter vector of interest according to initial conditions.

Errors are assumed to be jointly distributed as four-variate normal with zero mean, unit variances and free correlation coefficients: ${\left( {u_{{it - 2}} \varepsilon _{{it}} ,\xi _{i} ,v_{{it}} ,} \right)} \sim N_{4} {\left( {0,\Omega } \right)}.{\left( {i = {\text{l}} \ldots n} \right)}$

Likelihood contributions take the following form:

$$ L_{i} = {\left[ {\Phi _{4} {\left( {\Xi _{{{\left( 1 \right)}i}} ;\;\Omega } \right)}^{{L_{{it - 2}} }} \times \Phi _{4} {\left( {\Xi _{{{\left( 2 \right)}i}} ;\;\Omega } \right)}^{{H_{{it - 2}} }} } \right]}^{{R_{{it}} }} \times \Phi _{3} {\left( {\Xi _{{\_Lti}} ;\;\Omega _{{\_Lt}} } \right)}^{{{\left( {1 - R_{{it}} } \right)}}} , $$

(11)

where $\Phi _{j}$ denotes the j-variate normal${\text{c}}{\text{.d}}{\text{.f}}{\text{., }}L_{i} \Xi _{{{\left( k \right)}i}} ,\;k = 1,2,$ the vector of index functions for individual i, whose low pay transition component switches according to initial conditions, and the _Lt subscript denotes vectors and matrices deprived of elements referring to the low pay transitions equation.

Computation of multivariate normal distributions is performed by applying the Geweke–Hajivassiliou–Keane (GHK) simulator, yielding a maximum simulated likelihood (MSL) estimator.

Table 4 presents results in terms of marginal effects on estimated low pay persistence (p _it ) and entry (e _it ) probabilities, computed as:

$$ p_{{it}} = \frac{{\Phi _{3} {\left( {\Xi _{{{\left( 1 \right)}\_Si}} ;\,\Omega _{{\_S}} } \right)}}} {{\Phi _{2} {\left( {\Xi _{{\_Lti\_Si}} ;\,\Omega _{{\_Lt\_S}} } \right)}}}\quad ;\quad e_{{it}} = \frac{{\Phi _{3} {\left( {\Xi _{{{\left( 2 \right)}\_Si}} ;\,\Omega _{{\_S}} } \right)}}} {{\Phi _{2} {\left( {\Xi _{{\_Lti\_Si}} ;\,\Omega _{{\_Lt\_S}} } \right)}}} $$

(12)

where a _S subscript denotes vectors and matrices deprived of elements referring to the education equation. (Because these probabilities are not truncated upon education, the individual specific educational effect $\xi _{i}$ i integrates out, so that their evaluation only requires trivariate and bivariate normal integrals.) The effect considered is the one induced on transition probabilities by changes in the elements of z _it−2 relative to the reference person described in the text. Note that such changes will, in general, also affect the conditioning events, therefore complicating the interpretation of the effects estimated. To circumvent those complications, I fixed the probabilities of conditioning events at their sample averages, using the arguments of those average probabilities into the transition rates given in Eq. 12.