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The opinions expressed on this page are mine alone. Any similarities to the views of my employer are completely coincidental.

Tuesday, 6 September 2011

Taking the rough with the smooth - social mobility

My attention has been drawn to the latest issue of Sociological Research Online (apologies if you can't penetrate the pay wall). It contains amongst other things an article by Professors Li and Devine about social mobility in Britain. I was sent an early draft of the paper late in 2009 by Professor Devine and invited to comment, which I did. In brief I didn't like the paper much. They took some data that John Goldthorpe and I had already analyzed, estimated more or less the same models, obtained more or less the same results as we did but, to my mind, miraculously drew quite different conclusions - some of which were flatly contradicted by their own numbers. The published version has been improved cosmetically and a couple of the crasser errors have been expunged but otherwise most of my original criticisms still seem to hold water. Still, I should complain? At least it is a citation. For anyone with the remotest interest in the issue I reproduce below my comments on the original version of the paper (I've corrected a couple of minor typos):

Dear Fiona

Thanks for letting me see the paper. I'm a bit pushed for time right now so I have just glanced at it very quickly. If I get an opportunity before Christmas I'll try to read it more carefully. My immediate reaction is along the following lines:

In terms of relative rates - your results don't appear to differ from those that John and I get in our 2008 paper.  We find a small and marginally (statistically) significant  - as judged by the conditional likelihood ratio test - increase in fluidity for men. As judged by the approximate confidence interval around the "unidiff" parameter the difference isn't significant. We prefer to be cautious about how one should interpret such results in a two point comparison - indeed part of the point of our paper is to urge caution when drawing conclusions about long term trends based on just two data points. What our longer series shows quite clearly is that there are year on year fluctuations in the estimates of the unidiff parameter which are probably due to non sampling sources - ie differences in the way data are collected by different survey agencies using different instruments, different data processing conventions etc. Add to this the measurement error introduced by the various approximations that have to be made to produce similar occupational codings and an allowance for the fact that the data are not collected by SRS and you have to concede that all our (and your) significance tests err on the side of finding differences and all confidence intervals are too short. Incidentally what you say on page 25 in interpretation of the unidiff parameter isn't quite right: ", indicating a slight but significant increase in fluidity (the odds ratio for this would be e-.03 = .97)". This isn't an odds-ratio it is the amount by which all the log-linear interaction parameters are multiplied by in t2 compared to t1.

Contrary to your footnote 9 it is not the case that "...even the upper bounds of the 95% confidence intervals for the estimates are mostly below the 1972 benchmark (Goldthorpe and Mills 2008: Figure 7)". For the 72-92 series there are 12-1=11 relevant confidence intervals and of these by my visual inspection 9 intersect the 1972 baseline - the exceptions are 1979 and 1985. Your final sentence in footnote 9 must also be based on a misunderstanding. You say: "If the starting point of the 1991-2005 series were placed at the estimate point for GHS 1991, then the 2005 estimate and the upper bound would both fall well below the 1972 mark." But you fail to notice that our 1991 BHPS 7 class estimate has already been recalibrated so that the unidiff parameter for that year equals 0 and that is the only comparison with 2005 that is logically possible. It would be absurd to place the 7 class BHPS point at the same level as the 1991 GHS point and make a comparison with any points in the prior 1972-92 series. The point is, as I thought we  went to some trouble to explain, the two series are not comparable with respect to level.

Of course, as you know, the unidiff model is a very global test of differences between tables in that it considers all odds-ratios. I've looked in a little more detail at specific sets of odds-ratios and it is possible to find some slight evidence of a weakening in Erikson and Goldthorpe's so called "hierarchy" parameters though not in other parts of the CASMIN core model. If one really wanted to find evidence for more fluidity that is where I would look, but one still has to be mindful of the fact that one only has 2 data points. One also needs to be mindful of what the magnitude of change implies in terms of % changes in observed mobility rates. At the end of the day finding statistically significant differences just tells you about how much data you happen to have available. What you really want to know is how important substantively are  changes/differences implied by the model. That is what we do in footnote 25 of our 2008 paper and we conclude that such changes as can be attributed to an increase in social fluidity per se are of trivial magnitude when converted into percentage differences in the proportions making various transitions.

Moving on to "absolute" rates of mobility the differences in levels between your paper and our 2008 paper are  generated as far as I can see by your different way of defining upward and downward mobility. I find it odd that in your conclusions you say: "Crucially, contrary to Goldthorpe and his colleagues, we have argued that focusing on total rates of absolute mobility is misleading because it conceals upward and downward mobility." Nowhere in our 2008 paper do we focus only on total mobility rates - as is clear we also look at upward and downward mobility and you really musn't imply that we do not.  We do however use a rather conservative way of doing it - so for example moving from from NS-SEC 1 to NS-SEC 2 would not count as downward mobility in the 2008 paper (see our Table 1). There is obviously no "correct" way to do it and both ways have their merits.

Basically we seem to be in agreement though as far as women are concerned. You  however believe that you find something different for men. Broadly speaking our way of doing absolute upward and downward mobility doesn't produce any remarkable differences for men between 1991 and 2005. You find no significant difference in upward mobility (which bizarrely you contradict in your conclusions: "When unchanging total rates are disaggregated, the results show that men’s upward mobility is changing and on the decline.") , a 4.7% difference in downward mobility and  a -1.6% difference in horizontal mobility. Leaving aside how much variability we might see in these numbers if we were able to observe year on year change - these don't strike me as large differences.

However, let's assume that they are real and substantively important. I would then interpret them not, as you appear to do as evidence in favour of a Machin and Blanden -things are getting more unequal - story but as evidence of the contrary. Look at your Table IV. The mobility chances of men from 6 and 7 origins of getting into 1 and 2 destinations all improved (albeit slightly). The chances of men from 1 and 2 origins ending up in destinations 6 and 7 also increased. In other words this is consistent with the slight, but substantively trivial,  increase in fluidity result that we both find when we examine relative rates. Given that the origin and destination marginal distributions don't change that much over the two periods you would expect somewhat similar patterns in absolute and relative rates. So if there is any change over time it is in the direction of more - not less mobility. In short if you understand your own numbers in Table IV correctly I find it very difficult to understand how you can conclude that: "To repeat, these findings are similar to Blanden et al.’s research on social mobility focusing on income mobility." They most assuredly are not. They are entirely consistent with a hypothetical situation in which bright working class kids from the bottom of the class structure increased their chances of getting managerial and professional jobs whilst thick kids from the professional and managerial classes were unable to get the same types of jobs as their parents. Whilst it may be inconvenient politically for New Labour to approve of something along these lines, it is indeed  one of the things that  wanting to increase social fluidity might imply.   It is also worthwhile pointing out that Machin and Blanden's analysis of quintile tables implies a relative view of mobility rates - which we point out in our footnote 9 (2008) so the evidence of your analysis of absolute rates has little if any direct bearing on their results.

In short then I don't really see that your paper adds very much to what we did in our 2008 paper. Most of the results are very similar. You cetainly interpret your results in a different way, but I believe that your numbers don't  support that interpretation. For what it is worth I also think that in one respect our own work is not inconsistent with that of Machin and Blanden. That is that neither they nor we believe that there is terribly strong and convincing evidence that over the period from the early 1970s onward the social fluidity/mobility regime in GB has become  substantially more open. Our analysis and your analysis of class mobility show that for men (and incidently households - see our figure 9) there might be a very slight tendency in that direction - but that quantitatively it doesn't amount to much and could easily be the result of poorer quality measurement, lower response rates etc in the more recent period. What clearly is not the case in either your or our analysis is that there is any evidence of an increase of the association between class background and class destination between 1991 and 2005. Though this is not irreconcilable with Machin and Blanden's account of social mobility, they are after all taking about two specific cohorts and different destination periods, it seems just perverse to say that such a result strengthens their claim about long term trends. In short then, at the moment, in my opinion your contribution doesn't really throw any more light on the important issues and if anything, to mix my metaphors, significantly muddies the waters.
Hope this is helpful
all best

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