Abstract
A recent study by Fok et al. (Oxf Bull Econ Stat 77:872–896, 2015) concludes that there is a low-pay no-pay cycle for males and females in the Australian labour market. This note re-estimates the model of that study using the same data. It is found that Fok et al. (2015) conclusion is based on a model specification that assumes zero correlation of unobserved heterogeneity between the different labour force states modelled. The results of this note show that when the zero correlation restriction is relaxed, there is no evidence of a low-pay no-pay cycle for either males or females. It is also found that the marginal effect estimates used in Fok et al. (2015) to draw the low-pay no-pay cycle conclusion for males and females have been estimated imprecisely. Furthermore, contrary to what Fok et al. (2015) have concluded, the results of this note show that there is no evidence on heterogeneity in the low-pay no-pay cycle across the demographic subgroups examined by Fok et al. (2015).
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Notes
There is evidence of stepping stone effects from the results of this note as well. The difference of the marginal effects between lagged low-pay and lagged unemployment in the high-pay equation gives the stepping stone effect estimate. From Panel (b) in Table 1, for males the effect is about 3 percentage points, and for females about 10 percentage points. Comparing the results between Panel (b) and Panel (a) suggests that whether accounting for the correlation of the random effects does not change the estimates for the stepping stone effects much.
There is a sizable body of the literature examining low-paid employment with a focus on the state dependence of low pay—that is, whether and to what extent current low-paid employment increases the probability of remaining in low pay in the future. See, for instance, Sloane and Theodossiou (1998), Stewart and Swaffield (1999), Cappellari (2007) and Clarke and Kanellopoulos (2013).
Arguably, once it is established that there is not an overall low-pay no-pay cycle, to further investigate whether such a cycle exists in demographic subgroups; it is preferable to estimate the model separately for the subgroups of interest rather than to estimate a population model that includes the interaction terms. The preferred approach was not taken here due to the replication nature of this note.
See Baltagi (2013) for a detailed explanation of the estimator.
This is confirmed with the authors of FSW2015 through email communication.
Since lagged high-paid employment is the reference category, \( {\text{LP}}_{i,t - 1} = 0\; {\text{and}} \;{\text{UN}}_{i,t - 1} = 0 \) mean that the individual was in high-paid employment in year t − 1.
It was experimented to calculate the marginal effects by ignoring unobserved heterogeneity, but for the model with the zero correlation restriction the results were not as close to that of FSW2015 as those reported in this note. This suggested that FSW2015 could have accounted for unobserved heterogeneity in calculating the marginal effects. Nonetheless, the results of the marginal effect calculation without unobserved heterogeneity do not change the conclusions of this note.
For each draw of the parameters from their estimated distribution, the 250 Halton sequence draws are used to ‘integrated out’ unobserved heterogeneity. Therefore, the marginal effect estimates were calculated 125,000 (= 250 × 500) times in total in the process of bootstrapping the standard errors.
Indeed, the fact that there may be different ways to deal with unobserved heterogeneity in estimating the marginal effects adds an additional source of uncertainty, which further highlights the need to include a measure of stand error estimates for the marginal effect estimates.
The only information provided about estimation methodologies in FSW2015 is as follows: ‘The model parameters are obtained by maximum simulated likelihood estimation of the random effects logit model using the NLOGIT programme in the econometric software Limdep’. Therefore, there is no information on the simulation approach. The NLOGIT User’s Guide (student version), which is available online, does not provide sufficient information either.
For record, 250 Halton sequence draws are used to simulate the likelihood function in this note with the prime 2 and 3 used, respectively, for the unemployment and low-paid employment equations; the first 10 sequence numbers are discarded; and no antithetic draws are used. Experiments suggest that using the primes 2 and 3 to generate the Halton sequence draws produces the closest results to FSW2015’s, but the conclusions of this note remain when the pair of primes (5, 7) and (11, 13) were used.
These comparison results for the other variables can be obtained from the author on request.
Only the marginal effect estimates for the interaction terms are presented in Table 3 since they are used to infer heterogeneity in the low-pay no-pay cycle across demographic subgroups. The marginal effect estimates for all the other variables can be obtained from the author on request.
See footnote 8 in FSW3015.
The figures in Table 6 of FSW2015 need to be divided by 100 to be comparable with the figures here in this note since FSW2015 present their results in percentage terms.
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Acknowledgements
The paper uses the data in the confidentialised unit record file from the Australian Department of Social Services’ (DSS) Household, Income and Labour Dynamics in Australia (HILDA) Survey, which is managed by the Melbourne Institute of Applied Economic and Social Research. The findings and views reported in the paper, however, are those of the author and should not be attributed to either the DSS or the Melbourne Institute. I would like to thank Roger Wilkins, Rosanna Scutella, Yin King Fok, Wang Sheng Lee and Mark Wooden for their comments on earlier versions of the paper.
Data and computer code availability
The data that support the findings of this study are from the Melbourne Institute of Applied Economic and Social Research of the University of Melbourne, but restrictions apply to the availability of these data, which were used under licence for the current study, and so are not publicly available. Instructions for how other researchers can obtain the data and all the information needed to proceed from the raw data to the results of the paper (including code) are, however, available from the author upon request.
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Cai, L. Is there a low-pay no-pay cycle in Australia? A note on Fok, Scutella and Wilkins (2015). Empir Econ 59, 1493–1511 (2020). https://doi.org/10.1007/s00181-019-01663-y
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DOI: https://doi.org/10.1007/s00181-019-01663-y