## 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.

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## Notes

Estimates of income mobility have recently proven useful for evaluating the need for redistribution through taxation (Alesina and La Ferrara (2005).

See Heckman (1981a) for a seminal contribution on state dependence in dynamic econometric models of labour market outcomes.

I am discussing regression-type models for earnings transition probabilities. Alternative approaches in the mobility literature are those based on lifetime inequality indices or stochastic processes for individual earnings profiles (see, e.g. Buchinsky and Hunt 1999 and Moffitt and Gottschalk 1995 for applications).

Similar conclusions were reached by Cappellari (2002) who applied that model to Italian data for the early 1990s.

See D’Alessio and Faiella (2000) for a general description of the survey.

Given the Italian family-based system of taxation, net earnings not only reflect productivity and the features of the labour market but also family circumstances, so that in the analysis it will be important to account for household structure.

I also analysed monthly earnings and found results to be similar to those obtained on hourly earnings. Results obtained using monthly earnings are available upon request.

To assess the robustness of results to the choice of the low pay cut-off, I estimated the model using alternatively a lower and a higher threshold, namely, two-thirds of the median and the third decile. Findings from these supplementary analyses indicate that the results of the paper are not sensitive to the choice of the low pay threshold, and are available upon request.

See Wooldridge (2005) for an alternative approach.

Such an approach, based on the pooling of observations across transitions, is equivalent to the one of the pooled probit estimator discussed, e.g. by Woolridge (2002, chapter 13).

Before 1969, students from technical secondary schools who wanted to enrol into college had to go through a special examination. The reform abolished the exam, equalizing enrolment requirements of technical and general schools students (see Brunello and Miniaci 1999 for a discussion).

Individuals in the sample completed their educational investments before a set of reforms of secondary and tertiary education was put in place in the late 1990s/early 2000s, somehow modifying the classification of degrees and the mapping between degrees obtained and years of education. The SHIW variable also records (but only from 1995 onwards) whether individuals have a vocational qualification that can be obtained with two or three years of vocational training after lower secondary schools, whether they obtained a short (2 years) college diploma, and postgraduate qualifications.

The indicator function I(

*A*) takes value 1 whenever its argument is true and 0 otherwise.One might also think of \(l^{ * }_{{it - 2}} \) as a monotonic unspecified transformation of individual earnings, such as the normality assumption holds (Stewart and Swaffield 1999).

Firm size in the SHIW is recorded in classes, and the threshold that triggers variations in the intensity of employment protection legislation (i.e. 15 employees) falls within one of such classes (5 to 19).

Including the square of experience in the transition equation did not produce statistically significant estimates of the associated coefficient.

Four-dimensional normal integrals required for estimation are evaluated via simulation using the GHK simulator. Likelihood contributions are provided in the Appendix.

Similar results were obtained by following the testing strategy of Stewart and Swaffield (1999), who considered the restriction on squared labour market experience as the identifying one.

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## Acknowledgements

Thanks are due to Wiji Arulampalam, Carlo Dell’Aringa, Stephen Jenkins, Claudio Lucifora, Mark Stewart, the editor Christian Dustmann and two anonymous referees for very helpful comments. Financial support from the Nuffield Foundation (New Career Development Scheme) is gratefully acknowledged. Usual disclaimers apply.

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*Responsible editor*: Christian Dustmann

## Appendix

### 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:

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:

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:

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.

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Cappellari, L. Earnings mobility among Italian low-paid workers.
*J Popul Econ* **20**, 465–482 (2007). https://doi.org/10.1007/s00148-006-0065-z

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DOI: https://doi.org/10.1007/s00148-006-0065-z

### Keywords

- Low pay
- Earnings mobility

### JEL Classification

- C35
- D31
- J31