A mixed latent class Markov approach for estimating labour market mobility with multiple indicators and retrospective interrogation
Section 5. Results: Mixed LCM model with covariates and correlated measurement errors

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The results shown in the previous section showed that a mixed LCM model gives a better fit to our data. Like the standard LCM model, it takes into account misclassification and the pattern of missing data assuming the latter at random, and also includes unobserved heterogeneity. Assuming that data are missing at random is explained by the fact that each rotation group is observed in two quarters, but not in the two subsequent quarters, and also that these data are missing by design and do not depend on respondents’ true or reported status or other unobserved variables. In estimating our models, we simultaneously used information from all rotation groups, i.e., a Full Information Maximum Likelihood approach. Evidence from the observed gross flows, especially the fact that observed mobility is quite different between men and women and across ages (Table 3.5) indicated estimating a mixed LCM model with these two covariates affecting latent transitions.

Various models were estimated with the common following characteristic: mover-stayer and latent transitions follow a first-order Markov chain. In order to specify the measurement model, the following considerations were made: (i) the answer to the question on self-perceived condition in the labour market is given in the same interview after respondents answer the questions on which the ILO indicator is based; (ii) however, the ILO indicator is determined by ISTAT according to answers given to a series of questions following ILO guidelines, whereas S represents respondents’ self-perceptions: it is plausible that respondents are not aware of the ISTAT classification; (iii) indicator S and the indicator resulting from retrospective interrogation describe a more stable labour market than that of ILO and show the highest level of consistency: respondents may be influenced by the answers they gave the previous quarter; (iv) information for R is collected one year after answers to ILO and S; (v) for individuals who are in a steady state, reporting labour force condition correctly is an easier cognitive task than for those who experience at least one change, and may consequently show higher probabilities of giving incorrect answers.

Among the various possible specifications, the best-fitting model, for all analysed years, was to assume that stayers report their labour market condition correctly and that, for movers, measurement errors are constant over time and that the two indicators based on self-perception, S and R, are correlated, i.e., a direct effect between these two indicators is inserted in the model specification. (All estimated models were identified and, in order to avoid local maxima, estimation was performed several times with different sets of starting values; to estimate more parsimonious models, all three variable interactions were set at 0.) As an example, Tables 5.1 to 5.3 list some of the estimation results: labour market composition and estimated flows for the overall population, movers and stayers together, (The complete set of estimation results is available from the authors.) and estimated measurement errors. On average, over the five years, the percentage of movers was 17.69.

The estimated labour market composition in the first quarter, compared with the observed one (Table 3.2), shows a percentage of unemployment slightly lower than that obtained with the two self-perception indicators and higher than that with the ILO indicator.

Estimated transitions describe a more stable labour market than that observed with all three indicators, with the only exception of two transitions (see Table 3.4). Estimated gross flows are much more similar to those observed with self-perception and retrospective questions than those observed with the ILO indicator. This evidence also appears from the estimated measurement error (Table 5.3). An immediate objection to this result would be that we used two very similar indicators (the two self-perceptions) and a third one which was quite different (ILO). In fact, a similar result - lower measurement errors for self-perception than for the ILO indicator - was obtained by estimating an LCM model with only two indicators per latent variable: ILO and self-perception.

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