Abstract
This paper considers how the effect of job displacement varies across different individuals. In particular, our interest centers on features of the distribution of the individual-level effect of job displacement. Identifying features of this distribution is particularly challenging—e.g., even if we could randomly assign workers to be displaced or not, many of the parameters that we consider would not be point identified. We exploit our access to panel data, and our approach relies on comparing outcomes of displaced workers to outcomes the same workers would have experienced if they had not been displaced and if they maintained the same rank in the distribution of earnings as they had before they were displaced. Using data from the Displaced Workers Survey, we find that displaced workers earn about $157 per week less, on average, than they would have earned if they had not been displaced. We also find that there is substantial heterogeneity. We estimate that 42% of workers have higher earnings than they would have had if they had not been displaced and that a large fraction of workers have experienced substantially more negative effects than the average effect of displacement. Finally, we also document major differences in the distribution of the effect of job displacement across education levels, sex, age, and counterfactual earnings levels. Throughout the paper, we rely heavily on quantile regression. First, we use quantile regression as a flexible (yet feasible) first step estimator of conditional distributions and quantile functions that our main results build on. We also use quantile regression to study how covariates affect the distribution of the individual-level effect of job displacement.
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Notes
See Carrington and Fallick (2017) for a good discussion of reasons for why earnings may decline following job displacement.
A related (though distinct) idea is to compare the distribution of observed outcomes for displaced workers to their counterfactual distribution of outcomes if they had not been displaced. Researchers often compare the quantiles of these two distributions—this class of parameters is called quantile treatment effects. However, these types of parameters are likely to have severe limitations for understanding heterogeneous effects of job displacement which we discuss in more detail in the next section.
We note that other approaches could be used for identification here; for example, one could assume that treatment is as good as randomly assigned after conditioning on covariates and lagged outcomes or one could assume a conditional version of the Change in Changes model (Athey and Imbens 2006) as in Melly and Santangelo (2015).
See also Melly and Santangelo 2014 for an example of imputing missing wages using Change in Changes.
An alternative way to think about this is asking the question: What is an individual’s earnings following job displacement relative to what they earned before they were displaced? This sort of question does not require any identifying assumption (both of these are observed outcomes), but it has the limitation that this difference likely mixes effects of job displacement with trends in earnings over time.
This is essentially the setup in the case of our application on job displacement due to the Displaced Workers Survey being administered only every other year. In addition, part of our identification argument utilizes a Difference in Differences-type identification strategy. This sort of identification strategy identifies effects for individuals who move from being untreated to treated over time. It does not identify effects for individuals who are treated in the first period; moreover, this group is not used for identifying counterfactual outcome distributions (see discussion below) and therefore can be dropped from the analysis.
Farber (2017, Section 7) considers the fraction of displaced workers who have higher earnings following displacement than they did in their previous job which is similar to what we propose here.
Identifying these distributions typically either requires experimental data or some identifying argument. However, there are many approaches that are available in the econometrics literature for identifying these distributions; e.g., Firpo (2007) under selection on observables, Abadie (2003); Frolich and Melly (2013); Wüthrich (2019) when a researcher has access to an instrument, Athey and Imbens (2006); Bonhomme and Sauder (2011); Melly and Santangelo (2015); Callaway et al. (2018); Callaway and Li (2019) when a researcher has access to more than one period of data. The latter set of papers is most relevant in the current application.
This sort of issue is well known in the econometrics literature (e.g., Heckman et al. 1997). In other cases, comparing these two distributions may be very useful for policy evaluation or to perform social welfare calculations (Sen 1997; Carneiro et al. 2001). However, this does not apply for job displacement primarily because job displacement is not a “policy” (if it were, our results would indicate that it is a really bad policy). Instead, the reason why researchers would be interested in distributions here is to examine heterogeneous effects as we do in the current paper, and simply comparing the marginal distributions is of limited usefulness in this case.
Households in the CPS are usually interviewed for four consecutive months, are out of the sample for the next eight months, and then interviewed for another four months. After the eighth time participating, they leave the sample. Households that are interviewed in the fourth or eighth month (which are called outgoing rotation groups) are asked additional labor market questions. Thus, using our approach, we observe earnings for the untreated group in two consecutive years, but they can be different months for different individuals.
The distribution depends on the value of the covariates; the figure reports the average of the distribution over all values of covariates for displaced workers in the dataset. This is a standard way of converting conditional effects into unconditional effects.
It is worth explaining more why the distributions are so similar. The change in earnings over time is given \(Y_{it} - Y_{it-1}\) for displaced workers. The estimates in Figure 3 come from the distribution of \(Y_{it} - {\hat{Y}}_{it}(0)\) for displaced workers. Thus, any differences between the two distributions comes from differences between \(Y_{it-1}\) and \(Y_{it}(0)\). From Eq. 2, we generate \(Y_{it}(0) = Q_{Y_t(0)|X,D=1}(F_{Y_{t-1}|X,D=1}(Y_{it-1}|X_i)|X_i)\); in practice, this amounts to finding an individual’s rank in the conditional distribution of outcomes in time period \(t-1\) and applying the conditional quantile function for untreated potential outcomes to that rank. Also, notice that \(Y_{it-1} = Q_{Y_{t-1}|X,D=1}(F_{Y_{t-1}|X,D=1}(Y_{it-1}|X_i)|X_i)\); in other words, an alternative way to obtain an individual’s outcome in period \(t-1\) is to find their rank in the conditional distribution in time period \(t-1\) and apply the conditional quantile for outcomes in period \(t-1\) to that rank. Thus, any difference between the distribution of \(Y_{it} - Y_{it-1}\) and \(Y_{it} - Y_{it}(0)\) for displaced workers comes down to differences in the conditional quantiles (or distributions) of \(Y_{it}(0)\) and \(Y_{it-1}\). In our case, these two distributions are very similar – suggestive evidence of this can be found in Figs. 1 and 2—and this explains the reason for the high degree of similarity here.
It is perhaps surprising that such a large fraction of displaced workers appear to have higher earnings following displacement. Comparing pre- and post-displacement earnings of displaced workers, Farber (2017) similarly finds large percentages of workers earning more in their post-displacement job than in their pre-displacement job. Some possible explanations for this finding that he offers (and that likely apply to our case as well) are: (i) some displaced workers may have higher earnings but lower utility in their new job, (ii) search costs may keep workers from looking for new jobs that could potentially offer higher earnings, and (iii) risk aversion in the sense that workers have more information about their current job and may be reluctant to leave it for the possibility of a higher paying job when they have less information about other aspects of the new job. Another possible explanation is measurement error in earnings though Farber (2017) considers a sensitivity analysis related to measurement error and finds only fairly moderate changes to these results even under conservative assumptions on measurement error in earnings.
Recall that the outcome in these quantile regressions is \(Y_{it}(1) - {\hat{Y}}_{it}(0)\) for displaced individuals. This means that “large negative effects” occur at the lower quantiles in Fig. 4.
For the distribution of the effect of job displacement, there are some places where the estimate of this distribution using Change in Changes does fall outside of the 95% uniform confidence band using our original approach. However, despite the uniform confidence bands, the figure does not provide a formal test that the distributions are equal because it does not account for sampling uncertainty using Change in Changes.
This does imply that unconditional rank invariance does not hold here, but our assumptions have been about conditional rank invariance which is somewhat weaker.
Note that, besides Assumption 5, our other identifying assumptions hold by construction in this setup.
These are the quantile regressions that show up in the first step of our estimation procedure. We do use quantile regression in second step estimates, but it is not immediately clear how to adapt the Rothe and Wied (2013) test to that case due to there not being an observed distribution that we can directly compare to.
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Afrouz Azadikhah Jahromi declares that she has no conflict of interest. Brantly Callaway declares that he has no conflict of interest.
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We thank Guest Editor Blaise Melly and an anonymous referee for a number of helpful comments. We also would like to thank Michael Bognanno, Bernd Fitzenberger, Weige Huang, Moritz Ritter, Jungmo Yoon, and participants at the Economic Applications of Quantile Regression 2.0 Conference for their comments and suggestions.
Additional Tables and Figures
Additional Tables and Figures
1.1 2009–2010 Results
2009–2010 Quantile Regression Estimates of Job Displacement Effects on Covariates. Notes: QR estimates of the effect of covariates on the quantiles of the effect of job displacement in 2009-2010. The solid red horizontal lines provide OLS estimates of the effect of each covariate, and the horizontal dashed line contains a 90% confidence interval. The other multi-colored lines provide QR estimates of the effect of each covariate at particular quantiles from 0.1, 0.2, ..., 0.9. The shaded areas contain pointwise 90% confidence intervals from the quantile regressions
2009–2010 Quantile Regression Estimates of Job Displacement Effects on \(Y_t(0)\). Notes: QR estimates of the effect of what earnings would have been in the absence of job displacement, \(Y_t(0)\), on the quantiles of the effect of job displacement as discussed in the text in 2009-2010. The solid horizontal line provides OLS estimates of the effect of non-displaced potential earnings, and the horizontal dashed line contains a 90% confidence interval. The other line provides QR estimates of the effect of non-displaced potential earnings at particular quantiles from 0.1, 0.2, ..., 0.9. The shaded area contains pointwise 90% confidence intervals from the quantile regressions computed using the bootstrap with 1000 iterations
1.2 1997–1998 Results
1997–1998 Quantile Regression Estimates of Job Displacement Effects on Covariates. Notes: QR estimates of the effect of covariates on the quantiles of the effect of job displacement in 1997–1998. The solid red horizontal lines provide OLS estimates of the effect of each covariate, and the horizontal dashed line contains a 90% confidence interval. The other multi-colored lines provide QR estimates of the effect of each covariate at particular quantiles from 0.1, 0.2, ..., 0.9. The shaded areas contain pointwise 90% confidence intervals from the quantile regressions
1997–1998 Quantile Regression Estimates of Job Displacement Effects \(Y_t(0)\). Notes: QR estimates of the effect of what earnings would have been in the absence of job displacement, \(Y_t(0)\), on the quantiles of the effect of job displacement as discussed in the text in 1997–1998. The solid horizontal line provides OLS estimates of the effect of non-displaced potential earnings, and the horizontal dashed line contains a 90% confidence interval. The other line provides QR estimates of the effect of non-displaced potential earnings at particular quantiles from 0.1, 0.2, ..., 0.9. The shaded area contains pointwise 90% confidence intervals from the quantile regressions computed using the bootstrap with 1000 iterations
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Azadikhah Jahromi, A., Callaway, B. Heterogeneous Effects of Job Displacement on Earnings. Empir Econ 62, 213–245 (2022). https://doi.org/10.1007/s00181-020-01961-w
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DOI: https://doi.org/10.1007/s00181-020-01961-w
Keywords
- Job displacement
- Joint distribution of potential outcomes
- Distribution of the treatment effect
- Quantile regression
- Heterogeneous effects
- Rank invariance