A mixed latent class Markov approach for estimating labour market mobility with multiple indicators and retrospective interrogation
Section 4. Results: Comparisons of mixed and standard LCM models
We estimate various specifications of the standard and mixed LCM models. The standard model consists of two parts: structural, describing true dynamics among latent variables (true states) by a first-order Markov chain; and measurement, which links each latent variable to its indicators (observed conditions in the labour market). Some restrictions incorporating a priori information and/or assumptions are imposed on the parameters of the measurement part, based on evidence from observed data (inconsistencies and transitions) and on findings from the survey methodology and cognitive psychology literature on the error - generating mechanism. Only four of the nine rotation groups supplying information referring to one calendar year were interviewed in every quarter, and only for two of these groups do we have all three indicators of labour market conditions (see Table 3.1). For the other two groups, we do not have the information collected with the retrospective question. The pattern of missing information due to the rotation design of the survey is included in the estimated LCM models as data missing at random.
All estimated models share the following characteristics: true transitions follow a first-order Markov chain; (Due to the survey design, there were no individuals observed for three consecutive waves, i.e., a second-order Markov chain cannot be estimated, since the relative sufficient statistics are missing. However, although the labour market condition in one quarter may very plausibly affect the condition in the subsequent quarter, that it may do so in a significant manner after two quarters is far less plausible.) classification errors are assumed constant over time for each indicator; the ICE assumption is included. Model fit is evaluated by the BIC (Bayesian information criterion) index because of the large sample size (average 250,000 units per year; see Table 4.1)
The specification of a mixed LCM model is also recommended by the fact that the sample may contain various groups of respondents with different behaviour in the labour market. As already noted, the recent literature shows that not taking unobserved heterogeneity in transitions into account when estimating LCM models may result in biased estimates of measurement error (Magidson et al. 2007). In addition, a mixed LCM model may give the data a better fit.
We estimate a mover-stayer LCM model with the assumption of constant measurement errors across the two latent groups. It should be noted that all estimated models were identified and that, in order to reduce the risk of detecting local maxima, estimation was performed several times with different sets of starting values. Latent Gold 4.5 software was implemented (Vermunt and Magidson 2008).
Table 4.1 compares the mixed and standard LCM models fitted to our five data samples, referring to the years from 2005 and 2009 and using the BIC index. The mixed model shows a better fit for all samples. Table 4.2 lists the percentages of movers and stayers in the first quarter of 2005, and the distribution of the two unobserved groups in the first quarter of each year. Clearly, unobserved heterogeneity is highly correlated with the initial state and, as expected, stayers are either employed or not in the labour market, i.e., only a very small percentage is unemployed.
Year | n | Standard | Mixture |
---|---|---|---|
2005 | 220,051 | 650,241 | 649,401 |
2006 | 206,037 | 587,794 | 587,058 |
2007 | 274,484 | 748,788 | 748,654 |
2008 | 277,363 | 667,399 | 666,335 |
2009 | 274,723 | 747,997 | 746,991 |
Proportion | E | U | N | |
---|---|---|---|---|
Movers | 10.23 | 39.85 | 39.09 | 21.06 |
Stayers | 81.79 | 41.79 | 3.36 | 54.85 |
E = Employed, U = Unemployed, N = Not in the Labour Force. |
As the data in Tables 4.3-4.5 show, (Labour market composition, estimated transitions and estimated measurement errors show the same pattern in the other three quarters of each year.) the better fit to the data of the mixed model is all due to the different estimated transition rates; labour market composition and estimated measurement errors are the same in both models. This result is the opposite of that obtained by Magidson et al. (2007), who compared the mover-stayer and standard LCM models applied to labour market transitions from the Current Population Survey. The above authors found that the mixed LCM model provides a better fit to the data than the standard LCM model and that the latter, not taking unobserved heterogeneity into account, overestimates the degree of measurement error with respect to the mover-stayer model. In detail, the above authors used simulated results to estimate a violation of homogeneous transition probabilities, so that heterogeneity correlated with the initial state produces inflated estimates of measurement errors in a standard LCM model.
E | U | N | ||
---|---|---|---|---|
2005 | Standard | 41.67 | 7.00 | 51.33 |
Mixture | 41.59 | 7.02 | 51.39 | |
E = Employed, U = Unemployed, N = Not in the Labour Force. |
EE | EU | EN | UE | UU | UN | NE | NU | NN | ||
---|---|---|---|---|---|---|---|---|---|---|
2005 | Standard | 97.36 | 1.32 | 1.32 | 15.59 | 76.18 | 8.23 | 0.57 | 0.74 | 98.69 |
Mixture | 96.46 | 1.68 | 1.86 | 19.61 | 69.65 | 10.74 | 0.91 | 1.09 | 98.00 | |
2006 | Standard | 96.75 | 1.68 | 1.56 | 19.52 | 71.27 | 9.21 | 1.01 | 0.99 | 90.00 |
Mixture | 96.22 | 1.92 | 1.87 | 22.11 | 66.96 | 10.93 | 1.25 | 1.22 | 97.54 | |
2007 | Standard | 96.69 | 1.67 | 1.64 | 18.84 | 70.56 | 10.60 | 1.01 | 0.99 | 98.00 |
Mixture | 96.42 | 1.80 | 1.78 | 20.22 | 67.80 | 11.98 | 1.10 | 1.45 | 95.45 | |
2008 | Standard | 97.56 | 1.41 | 1.03 | 15.86 | 79.73 | 4.42 | 0.53 | 0.62 | 98.85 |
Mixture | 96.45 | 1.89 | 1.66 | 19.56 | 73.25 | 7.19 | 0.83 | 0.89 | 98.28 | |
2009 | Standard | 96.85 | 1.71 | 1.44 | 14.04 | 75.33 | 9.63 | 1.04 | 1.01 | 97.95 |
Mixture | 96.27 | 1.95 | 1.78 | 17.09 | 71.16 | 11.75 | 1.30 | 1.22 | 97.48 | |
EE = Employed in both quarters. EU = Employed in first quarter and Unemployed in second one. EN = Employed in first quarter and Not in the Labour Force in second one. UE = Unemployed in first quarter and Employed in second one. UU = Unemployed in both quarters. UN = Unemployed in first quarter and Not in the Labour Force in second one. NE = Not in the Labour Force in first quarter and Employed in second one. NU = Not in the Labour Force in first quarter and Unemployed in second one. NN = Not in the Labour Force in both quarters. |
EE | EU | EN | UE | UU | UN | NE | NU | NN | ||
---|---|---|---|---|---|---|---|---|---|---|
2005 | Standard | 99.82 | 0.01 | 0.17 | 6.17 | 45.04 | 48.80 | 0.89 | 0.50 | 98.61 |
Mixture | 99.82 | 0.01 | 0.17 | 6.16 | 45.06 | 48.78 | 0.90 | 0.51 | 98.59 | |
2006 | Standard | 99.83 | 0.01 | 0.16 | 6.50 | 41.92 | 51.58 | 0.75 | 0.45 | 98.80 |
Mixture | 99.87 | 0.01 | 0.13 | 5.17 | 37.28 | 57.55 | 0.68 | 0.40 | 98.92 | |
2007 | Standard | 99.75 | 0.01 | 0.24 | 6.84 | 39.83 | 53.34 | 0.75 | 0.47 | 98.79 |
Mixture | 99.75 | 0.01 | 0.24 | 6.77 | 39.92 | 53.31 | 0.77 | 0.47 | 98.76 | |
2008 | Standard | 99.83 | 0.01 | 0.17 | 3.81 | 42.45 | 53.74 | 0.61 | 0.38 | 99.02 |
Mixture | 99.83 | 0.01 | 0.17 | 3.82 | 42.41 | 53.76 | 0.62 | 0.38 | 99.00 | |
2009 | Standard | 95.34 | 0.98 | 3.68 | 18.30 | 41.17 | 40.53 | 2.06 | 1.61 | 96.33 |
Mixture | 95.22 | 2.34 | 2.44 | 15.60 | 68.02 | 16.37 | 1.74 | 2.14 | 96.13 | |
EE = Truly Employed and classified as Employed by ILO indicator. EU = Truly Employed but classified as Unemployed by ILO indicator. EN = Truly Employed but classified as Not in the Labour Force by ILO indicator. UE = Truly Unemployed but classified as Employed by ILO indicator. UU = Truly Unemployed and classified as Unemployed by ILO indicator. UN = Truly Unemployed but classified as Not in the Labour Force by ILO indicator. NE = Truly Not in the Labour Force but classified as Employed by ILO indicator. NU = Truly Not in the Labour Force but classified as Unemployed by ILO indicator. NN = Truly Not in the Labour Force and classified as Not in the Labour Force by ILO indicator. |
The mover-stayer model describes a more dynamic labour market, especially for unemployed respondents: the probability of remaining unemployed over the quarter is lower than that estimated by the standard model.
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