A mixed latent class Markov approach for estimating labour market mobility with multiple indicators and retrospective interrogation
Section 6. Concluding remarks
This paper presents a latent class approach to correct gross flows from correlated errors. The emphasis is on the capacity to account for correlated classification errors across panel data, due to the rotating design of the survey which generates patterns of missing data and of unobserved heterogeneity.
The latent class approach was applied to transitions in the Italian labour market among the three usual conditions of employed, unemployed and not in the labour force. The data refer to the years from 2005 to 2009 and were collected by the Continuous Italian Labour Force Survey on a sample of Italian households with a 2-2-2 rotating design over quarters. Information on labour force condition in one reference quarter was collected three times: (i) respondents were classified as employed, unemployed or not in the labour force according to the definition of the International Labour Office on the basis of answers to a selected group of questions; (ii) respondents were asked to classify themselves as employed, unemployed or not in the labour force (i.e., the self-perceived condition); (iii) a retrospective question asked about state in the labour market one year previously. This means that three indicators of labour condition were available. The three indicators gave quite different descriptions of the Italian labour market, revealing a significant degree of inconsistency. This evidence indicates measurement error in the data.
The best-fitting model was a mover-stayer LCM, in which latent transitions in the labour market follow a first-order Markov chain, stayers always report their market condition correctly; for movers, measurement errors were constant over time and correlated to the two self-perception indicators; the gender and age of respondents were included as covariates; the rotating design of the survey was treated as information missing at random. The model corrects observed gross flows towards a more stable labour market and estimates that the indicator of labour market condition based on the ILO definition is affected by the greatest degree of measurement error.
A second result found here is that, when unobserved heterogeneity occurs, a mixed LCM model fits the data better than the standard LCM model. This finding is consistent with other reports (e.g., Magidson et al. 2007). However, in our case, the two models estimate the same quantity of measurement error, the difference in fit being due to estimated flows. Instead, the above authors found an overestimation of measurement error when unobserved heterogeneity was not taken into account.
A final consideration regards the sample design of the survey, which is two-stage, as described in Section 3. In our analyses, we did not take into account the complex sample design, but estimated gross flows on the longitudinal population provided by the Italian Institute of Statistics. In subsequent research, it will be of interest to compare how results may be affected by incorporating methods for surveys on complex samples with our estimation strategy, an interesting reference to which was made by Lu and Lohr (2010).
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