Heterogeneous Effects of Job Displacement on Earnings
HHeterogeneous Effects of Job Displacement on Earnings
Afrouz Azadikhah Jahromi ∗ Brantly Callaway †‡ June 7, 2020
Abstract
This paper considers how the effect of job displacement varies across different individ-uals. In particular, our interest centers on features of the distribution of the individual-level effect of job displacement. Identifying features of this distribution is particularlychallenging – 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 exploitour access to panel data, and our approach relies on comparing outcomes of displacedworkers to outcomes the same workers would have experienced if they had not beendisplaced and if they maintained the same rank in the distribution of earnings as theyhad before they were displaced. Using data from the Displaced Workers Survey, wefind that displaced workers earn about $157 per week less than they would have earnedif they had not been displaced. We also find that there is substantial heterogeneity. Weestimate that 42% of workers have higher earnings than they would have had if theyhad not been displaced and that a large fraction of workers have experienced substan-tially more negative effects than the average effect of displacement. Finally, we alsodocument major differences in the distribution of the effect of job displacement acrosseducation 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 functionsthat our main results build on. We also use quantile regression to study how covariatesaffect the distribution of the individual-level effect of job displacement.
JEL Codes:
J63, C21
Keywords:
Job Displacement, Joint Distribution of Potential Outcomes, Distribution ofthe Treatment Effect, Quantile Regression, Heterogeneous Effects, Rank Invariance ∗ Assistant Professor, Department of Economics, Widener University, Email: [email protected]. † Assistant Professor, Department of Economics, University of Georgia, Email: [email protected] ‡ We thank Guest Editor Blaise Melly and an anonymous referee for a number of helpful comments. Wealso 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 commentsand suggestions. a r X i v : . [ ec on . E M ] J un Introduction
A typical finding in the job displacement literature is that “the effect” of job displacementis large and persistent (see, for example, Jacobson, LaLonde, and Sullivan (1993) and muchsubsequent work). However, considering a single effect of job displacement ignores potentialheterogeneity across individuals. Treatment effect heterogeneity is a general feature of manyprogram evaluation problems in economics, but treatment effect heterogeneity is likely to beparticularly important in the context of job displacement. In particular, some individualsmay be able to find similar jobs quickly after they are displaced, but other individuals mayexperience larger losses due to decreased match quality with their employer (e.g., Jovanovic(1979)), loss of firm-, occupation-, or industry-specific human capital (Topel (1991) andNeal (1995)), loss of a job at a high paying firm (Abowd, Kramarz, and Margolis (1999)),or failure to find full time work (Farber (2017)). In the current paper, we are interested intrying to distinguish between the cases where all individuals experience roughly the sameeffect of job displacement or where “the effect”of job displacement mixes together individualswho have relatively small effects of job displacement with individuals who experience largenegative effects of job displacement. Distinguishing between these cases is important for ourunderstanding of job displacement as well as being useful for targeting policy responses tojob displacement.Learning about treatment effect heterogeneity requires learning about the distribution ofthe treatment effect itself. And the distribution of the treatment effect itself depends, inturn, on the joint distribution of treated and untreated potential outcomes. Learning aboutthe joint distribution of treated and untreated potential outcomes is quite challenging –e.g., even if we could randomly assign workers’ displacement status, this would only identifythe marginal distributions not the joint – and has been the subject of a large literature ineconometrics. This literature includes Heckman, Smith, and Clements (1997), Fan and Park(2010), Fan, Guerre, and Zhu (2017), Frandsen and Lefgren (2017), and Callaway (2020),among others. This literature has largely focused on partial identification results underrelatively weak assumptions or invoking stronger assumptions to obtain point identification.In the current paper, we identify the joint distribution of earnings for displaced workers(their treated potential outcomes) and the outcomes they would have experienced if (i) they See Carrington and Fallick (2017) for a good discussion of reasons for why earnings may decline followingjob displacement. A related (though distinct) idea is to compare the distribution of observed outcomes for displaced workersto their counterfactual distribution of outcomes if they had not been displaced. Researchers often comparethe 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 jobdisplacement which we discuss in more detail in the next section. What these assumptionsmean in the context of job displacement is that (i) the path of earnings that displaced work-ers would have experienced had they not been displaced is the same as the path of earningsthat non-displaced workers with the same characteristics did experience, and (ii) if, for ex-ample, the largest increases in earnings for non-displaced workers tended to go to individualswith the highest earnings in the previous period, the same would have occurred for displacedworkers if they had not been displaced from their job.One challenge is that we cannot implement the estimation procedure proposed in Call-away, Li, and Oka (2018) because their approach is for the case with discrete covariates onlyand involves sample splitting. This is not feasible in the current application where thereare some continuous covariates (e.g., age) and too many discrete covariates relative to thenumber of observations to split the sample on every possible combination of the discretecovariates. Instead, we use quantile regression (Koenker and Bassett Jr (1978) and Koenker(2005)) to estimate each required conditional distribution / quantile function. Quantile re-gression provides a flexible way to model the conditional distributions and quantiles that weneed to estimate in the first step. After the conditional distributions of treated and untreated potential outcomes have We note that other approaches could be used for identification here; for example, one could assume thattreatment is as good as randomly assigned after conditioning on covariates and lagged outcomes or one couldassume a conditional version of the Change in Changes model (Athey and Imbens (2006)) as in Melly andSantangelo (2015). Other papers that have used quantile regression as a first-step estimator include Melly and Santangelo(2015) and W¨uthrich (2019). This step results in observed post-displacement earningsbeing matched with an estimate of earnings in the absence of displacement. Once this stephas been completed, we can obtain any feature of this distribution. This also implies thatthe distribution of the effect of job displacement conditional on covariates is identified aswell. In a final step, we again use quantile regression to summarize how the effect of jobdisplacement varies with covariates at different parts of the conditional distribution.We use the Displaced Workers Survey (DWS) which is a supplement to the CurrentPopulation Survey (CPS) to estimate the entire distribution of the effect of job displacementon weekly earnings for displaced workers and evaluate how the effects of job displacement varyacross individuals with different observable characteristics (e.g., age, sex, race, education,and marital status) and as a function of what a displaced worker’s earnings would have beenin the absence of job displacement. Our main results use the 2016 DWS. We find that, onaverage, displaced workers lose about $157 per week relative to what they would have earnedif they had not been displaced (this corresponds to 18% of pre-displacement earnings). Wealso find that there is substantial heterogeneity. We estimate that 42% of displaced workershave higher earnings following displacement than they would have had if they had not beendisplaced and maintained their rank in the earnings distribution over time. On the otherhand, we also estimate that 21% of workers earn at least $500 less per week than they wouldhave earned if they had not been displaced and had maintained their rank.These results suggest that the effect of job displacement can be much more severe than theaverage effect for some workers who are the most negatively affected while being quite mildfor other workers. In a final step, we use quantile regression to study the effect of covariateson the distribution of the individual-level effect of job displacement. We find substantialheterogeneity across observed characteristics. The largest effects of job displacement appearto be concentrated among older, male, college graduates as well as those who would have hadhigh earnings if they had not been displaced. As an additional check, we compare our resultsto those obtained under the condition that a worker who is displaced from their job wouldhave earnings that are exactly equal to their pre-displacement earnings. We also extend our 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 followingjob displacement relative to what they earned before they were displaced? This sort of question does notrequire any identifying assumption (both of these are observed outcomes), but it has the limitation that this
Related Work on Job Displacement
Our work is related to a large literature on job displacement. We only briefly survey themost relevant research here. Almost all work on job displacement considers a single “effect”of job displacement. This effect usually corresponds to an estimated parameter in an OLSregression. Much of the literature (e.g., Jacobson, LaLonde, and Sullivan (1993)) has beeninterested in the long-term effect of job displacement. This is particularly true for papersthat have used widely available panel data sets such as the NLSY and PSID (e.g., Ruhm(1991), Stevens (1997), and Kletzer and Fairlie (2003)) as well as administrative data (e.g.,von Wachter, Song, and Manchester (2009) and Couch and Placzek (2010)). On the otherhand, research that has used the Displaced Workers Survey has focused on short run effectsof job displacement because the DWS does not contain follow up interviews with displacedworkers. Thus, here, we consider only short-run heterogeneous effects of job displacement. Itwould be interesting to extend our approach to the long-term case though this would requirean alternative data source.Two strands of the literature are most related to the current paper. First, in a series ofwork (Farber (1997), Farber (2005), and Farber (2017)), Henry Farber has used the DWSto study the effect of job displacement. Broadly, the main concerns of these papers are theemployment and earnings effects of job displacement and how these have varied over time.Farber (2017) also considers the fraction of displaced workers whose earnings are higherfollowing job displacement than they were in their pre-displacement job. A primary differencebetween our main results and those in Farber (2017) is that we try to adjust for how earningsfor displaced workers would have evolved over time in the absence of job displacement. Ourresults that also use raw changes in earnings over time are also somewhat different; inparticular, Farber (2017, Section 7) focuses mostly on displaced workers that have movedback into full time work while we focus on all displaced workers that are still in the laborforce. In addition, we think about the entire distribution of the effect of job displacementand how the distribution of the effect of job displacement varies across covariates and varies difference likely mixes effects of job displacement with trends in earnings over time.
In this section, we discuss the parameters that we are interested in identifying and theassumptions required to identify them. But first, we introduce some notation. We considerthe case where a researcher has access to two periods of panel data which corresponds to theavailable data that we use from the Displaced Workers Survey. We denote the two periodsby t and t −
1. We define outcomes in each period by Y it and Y it − . Individuals have treatedand untreated potential outcomes, Y is (1) and Y is (0), for s ∈ { t, t − } ; these correspondto the outcomes that a particular individual would experience if they were displaced ornot displaced at a particular point in time. We consider the case where no one is treatedin the first period and some individuals become treated in the second period. Let thevariable D i denote whether or not an individual is treated (i.e., displaced). Thus, we observe Y it = D i Y it (1) + (1 − D i ) Y it (0) and Y it − = Y it − (0). Define ∆ Y it := Y it − Y it − and ∆ Y it (0) := Y it (0) − Y it − (0). We also observe some covariates X i that include a worker’s race, sex,education, age, and marital status.Our interest centers on features of the distribution of ( Y t (1) − Y t (0) | D = 1). This is thedistribution of the treatment effect conditional on being part of the treated group. In otherwords, it is the distribution of the difference between earnings of displaced workers following This is essentially the setup in the case of our application on job displacement due to the DisplacedWorkers Survey being administered only every other year. In addition, part of our identification argumentutilizes a Difference in Differences-type identification strategy. This sort of identification strategy identifieseffects for individuals who move from being untreated to treated over time. It does not identify effects forindividuals who are treated in the first period; moreover, this group is not used for identifying counterfactualoutcome distributions (see discussion below) and therefore can be dropped from the analysis. Y it (1) or Y it (0) is observed but Y it (1) − Y it (0) is not observed forany individual. Parameters that depend on this distribution include many treatment effectheterogeneity-type parameters: (i) the fraction of displaced workers that have higher earningsfollowing displacement than they would have had if they had not been displaced, and (ii) howmuch lower earnings are for individuals who are most affected by job displacement, amongothers. We are also interested in features of the distribution of ( Y t (1) − Y t (0) | Y t (0) , D =1). These sorts of parameters include the distribution of the effect of job displacement fordisplaced workers as a function of what a displaced worker’s earnings would have been ifthey had not been displaced. Finally, we are interested in the distribution of the treatmenteffect for displaced workers as a function of covariates; i.e., features of the distribution of( Y t (1) − Y t (0) | X, D = 1). In particular, these parameters allow us to think about whatindividual-level characteristics are associated with the largest effects of job displacement.Our approach allows one to look at different parts of the conditional distribution of theeffect of job displacement which is substantially more informative than looking at averageeffects across different values of covariates which is commonly done in applied work (see, forexample, the discussion in Bitler, Gelbach, and Hoynes (2017)).What each of these parameters have in common is that they depend on the joint dis-tribution ( Y t (1) , Y t (0) | X, D = 1). By Sklar’s Theorem (Sklar (1959)), joint distributionscan be written as the copula (which captures the dependence of two random variables; seeNelsen (2007) for more details about copulas) of the marginal distributions. Thus, we takea two step approach to identifying this joint distribution. In the first step, we identify themarginal distributions F Y t (1) | X,D =1 and F Y t (0) | X,D =1 . In the second step, we impose additionalassumptions to additionally identify their joint distribution. The first step in our analysis is to show that F Y t (1) | X,D =1 and F Y t (0) | X,D =1 are identified. F Y t (1) | X,D =1 is immediately identified from the sampling process. It is just the conditionaldistribution of displaced potential earnings for the group of individuals that are displacedfrom their job – these are the earnings that are observed for displaced workers.On the other hand, identifying F Y t (0) | X,D =1 is substantially more challenging. This is thedistribution of earnings that displaced workers would have experienced if they had not beendisplaced. We make the following two assumptions:7 ssumption 1 (Distributional Difference in Differences) . ∆ Y t (0) ⊥⊥ D | X Assumption 2 (Copula Invariance Assumption) . Let C ∆ Y t (0) ,Y t − (0) | X,D = d denote the copulabetween the change in untreated potential outcomes and the initial level of untreated potentialoutcomes conditional on covariates and treatment status. Then, C ∆ Y t (0) ,Y t − (0) | X,D =1 = C ∆ Y t (0) ,Y t − (0) | X,D =0 a.s. Assumption 3 (Observed Data) . The observed data consists of { Y it , Y it − , X i , D i } ni =1 andare independent and identically distributed and where n denotes the sample size. Assumption 4 (Continuously Distributed Outcomes) . Y t (0) and Y t − (0) , are continuouslydistributed conditional on X and D = d for d ∈ { , } Assumptions 1 to 4 are the assumptions made in Callaway, Li, and Oka (2018) to identifythe counterfactual distribution F Y t (0) | X,D =1 . The first is a Difference in Differences assump-tion. It says that the distribution of the path of earnings that individuals who are displacedfrom their job would have experienced if they had not been displaced from their job is thesame as the distribution of the path of earnings that individuals that were not displaced fromtheir job actually experienced (after conditioning on covariates). The second assumption isa Copula Invariance assumption. It says that if, for example, we observe the largest earningsincreases over time going to those at the top of the earnings distribution for the group ofnon-displaced workers, then we would have observed the same thing for displaced workersif they had not been displaced (again, this is conditional on covariates). Assumption 3 saysthat we observe two periods of panel data that is cross sectionally iid. Assumption 4 saysthat untreated potential outcomes are continuously distributed. Importantly, in the caseof job displacement, Assumption 4 does not require that treated potential outcomes (i.e.,outcomes following displacement for displaced workers) be continuously distributed. Thisallows for some displaced workers to not be working following displacement which leads toa mass of workers with zero earnings. Callaway, Li, and Oka (2018) show that, under theseconditions F Y t (0) | X,D =1 ( y | x ) = P (∆ Y t + Q Y t − | X,D =1 ( F Y t − | X,D =0 ( Y t − | x ) | x ) ≤ y | x, D = 0) (1)where every term in Equation (1) is identified and Q ( · ) denotes the quantile function (i.e.,the inverse of the cdf). In other words, we can recover the distribution of outcomes that8isplaced workers would have experienced in the absence of displacement. And this impliesthat both marginal distributions of interest are identified. It is worth briefly consideringwhere the expression for this counterfactual distribution comes from. Omitting conditioningon covariates (for simplicity), notice that the counterfactual distribution F Y t (0) | D =1 ( y ) is givenby P ( Y t (0) ≤ y | D = 1) = P (∆ Y t (0) + Y t − (0) ≤ y | D = 1)= P ( Q ∆ Y t (0) | D =1 ( F ∆ Y t (0) | D =0 (∆ Y t (0))) + Q Y t − (0) | D =1 ( F Y t − (0) | D =0 ( Y t − (0))) ≤ y | D = 0)= P (∆ Y t (0) + Q Y t − (0) | D =1 ( F Y t − (0) | D =0 ( Y t − (0))) ≤ y | D = 0)The first equality adds and subtracts Y t − (0). The second equality is most interesting andholds under Assumption 2 which says that the joint distribution of (∆ Y t (0) , Y t − (0)) is thesame across displaced and non-displaced individuals after adjusting for differences in themarginal distributions – adjusting for differences in the marginal distributions is exactlywhat the two terms involving Q ( F ( · )) do. Finally, the third equality holds immediatelyby Assumption 1. Thus, the result in Equation (1) says that the distribution of outcomesthat displaced workers would have experienced in the absence of job displacement can beobtained from the distribution of earnings of non-displaced workers but only after “adjusting”for differences in the marginal distributions of earnings in the period before displacement aswell as accounting for changes in earnings over time experienced by non-displaced workers. Identifying the joint distribution of treated and untreated potential outcomes is a notoriouslydifficult challenge in the microeconometrics literature. Standard identifying assumptions (oreven random assignment of the treatment) do not identify this joint distribution. This sectiondescribes our approach to identifying this distribution. Define (cid:101) Y it (0) := Q Y t (0) | X,D =1 ( F Y t − | X,D =1 ( Y it − | X i ) | X i ) (2)Notice that F Y t − | X,D =1 ( Y it − | X i ) is a displaced worker’s rank in the conditional earningsdistribution in the period before anyone is displaced. Thus, conditional on our identificationarguments in the previous section for the counterfactual distribution, the transformation onthe right hand side of Equation (2) is available and (cid:101) Y it (0) is the outcome that a displacedworker would experience if they had not been displaced and if they had the same rank inthe earnings distribution as they did in the previous period.Immediately, Equation (2) implies that the joint distribution ( Y t (1) , (cid:101) Y t (0) | X, D = 1) is9dentified. One idea is to just call features of this joint distribution as the parameters ofinterest. In other words, without any additional assumptions, we can identify parameterssuch as the fraction of displaced individuals that have higher earnings than they would havehad if they had not been displaced and if they had maintained the same rank in the earningsdistribution as they had in the pre-treatment period.Alternatively, we can make the additional assumption:
Assumption 5 (Rank Invariance Over Time) . F Y t (0) | X,D =1 ( Y t (0) | X ) = F Y t − (0) | X,D =1 ( Y t − (0) | X )Assumption 5 says that, in the absence of job displacement, displaced workers wouldhave maintained their rank in the distribution of earnings over time. Assumption 5 impliesthat Y it (0) = (cid:101) Y it (0) and, thus, that the joint distribution ( Y t (1) , Y t (0) | X, D = 1) is identified,and we can obtain any features of this joint distribution. For comparison, identifying thisdistribution allows one to ask: What fraction of displaced workers actually benefit fromjob displacement without the additional caveat mentioned above. At any rate, employingAssumption 5 leads to exactly the same results as focusing on features of the joint distribution( Y t (1) , (cid:101) Y t (0) | X, D = 1) – only the interpretation is different. We use the notation Y it (0)rather than (cid:101) Y it (0) throughout the rest of the paper for simplicity but we interpret our resultscarefully in the application as the caveat of being conditional on having the same rank overtime likely applies. Remark 1.
An alternative approach is to define (cid:101) Y it (0) = Y it − (0) among displaced workers. In this case, one can immediately identify the joint distribution ( Y t (1) , (cid:101) Y t (0) | X, D = 1). Rel-ative to the previous case, there are some advantages and disadvantages to this approach.The main advantage is that it does not require Assumptions 1 and 2 as the distribution of( Y t (1) , (cid:101) Y t (0) | X, D = 1) is identified from the sampling process rather than requiring iden-tification assumptions. Without further assumptions, one can immediately identify thingslike: the fraction of displaced workers who have higher earnings following job displacementthan they had before they were displaced, etc. The main disadvantage is that, in this case, Y it (0) = (cid:101) Y it (0) seems less plausible. But, at any rate, this approach serves as a usefulcomparison. Remark 2.
Assumption 5 is distinct from the more commonly invoked “cross-sectional”rank invariance assumption – namely, that a displaced worker’s rank in the distribution of Farber (2017, Section 7) considers the fraction of displaced workers who have higher earnings followingdisplacement than they did in their previous job which is similar to what we propose here. it (1) (which is observed) is the same as their rank would be in the distribution of Y it (0)if they had not been displaced. This is a very strong (and implausible) assumption in thecurrent context as it rules out things like individuals not finding work following displacement. A common alternative strategy for trying to analyze heterogeneous effects of experiencingsome treatment is to compare the distribution of treated potential outcomes to the dis-tribution of untreated potential outcomes; in our case, this would mean comparing thedistribution of earnings that displaced workers actually experienced to the distribution ofearnings that they would have experienced in the absence of job displacement. Unlike ourmain parameters of interest, comparing these two distributions does not require identifyingthe joint distribution of treated and untreated potential outcomes – in fact, these are thetwo distributions that are identified using only Step 1 of our identification argument above.Often researchers invert these two distributions and take their difference. The result of thistransformation is a class of parameters called quantile treatment effects which are importantparameters in the program evaluation literature.In the context of job displacement, these types of parameters may have severe limita-tions. These limitations stem from the fact that individuals may have substantial differencesin their “rank” if they were displaced relative to if they were not displaced. This meansthat, although it is tempting to interpret differences between, for example, the 10th per-centile of displaced potential earnings and non-displaced potential earnings as the effect ofjob displacement for individuals at the lower part of the earnings distribution, this sort ofinterpretation is unlikely to be correct. The reason is that some individuals in the lowerpart of the earnings distribution might have had relatively high earnings if they had notbeen displaced. When some individuals remain unemployed or have substantially reducedhours following job displacement, this can systematically lead to larger differences between 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 thesedistributions; e.g., Firpo (2007) under selection on observables, Abadie (2003), Frolich and Melly (2013),and W¨uthrich (2019) when a researcher has access to an instrument, Athey and Imbens (2006), Bonhommeand Sauder (2011), Melly and Santangelo (2015), Callaway, Li, and Oka (2018), and Callaway and Li (2019)when a researcher has access to more than one period of data. The latter set of papers is most relevant inthe current application. This sort of issue is well-known in the econometrics literature (e.g., Heckman, Smith, and Clements(1997)). In other cases, comparing these two distributions may be very useful for policy evaluation or toperform social welfare calculations (Sen (1997) and Carneiro, Hansen, and Heckman (2001)). However, thisdoes not apply for job displacement primarily because job displacement is not a “policy” (if it were, ourresults would indicate that it is a really bad policy). Instead, the reason why researchers would be interestedin distributions here is to examine heterogeneous effects as we do in the current paper, and simply comparingthe marginal distributions is of limited usefulness in this case.
Given the identification results above, determining the best estimation strategy is still chal-lenging. Like many applications in economics, we have a relatively large number of covariatesthat we would like to condition on to make the identifying assumptions more plausible andonly a moderate number of observations. The first step is to estimate the counterfactualdistribution of untreated potential outcomes conditional on covariates for the treated groupas in Equation (1). This requires estimating three conditional distribution/quantile func-tions. These are challenging. Distributional assumptions about the distribution of outcomesconditional on covariates are likely to be invalid. On the other hand, implementing fully non-parametric estimators is infeasible in our case. Callaway, Li, and Oka (2018) consider thecase with only discrete covariates and propose nonparametric estimators based on splittingthe sample according to each possible combination of discrete covariates. This is infeasible inour case because we have some continuous covariates and the number of discrete covariatesis too large relative to the number of observations to split the sample. Instead, we proposeto estimate these conditional distributions/quantiles using quantile regression. In particular,we suppose that
Assumption 6 (Quantile Regression) . For all ( s, d ) ∈ { t, t − } × { , } , Y is (0) = Q Y s (0) | X,D = d ( U isd | X i ) = P sd ( X i ) (cid:48) β sd ( U isd ) with U isd | X i , D i ∼ U [0 , and where P sd ( X ) are some transformations of the vector of co-variates X . Assumption 6 suggests that we can estimate each of the terms in Equation (1) using quan-tile regression. In particular, consider the following algorithm to estimate the counterfactualdistribution in Equation (1) and estimate Y it (0) for each individual in our sample. Algorithm 1.
Let τ denote a fine grid of equally spaced elements between 0 and 1,12. Estimate ˆ Q Y t − | X,D =1 ( τ ) by quantile regression of Y it − on X i using displaced individ-uals2. Estimate ˆ Q Y t − | X,D =0 ( τ ) by quantile regression of Y it − on X i using non-displaced in-dividuals and invert to obtain ˆ F Y t − | X,D =0 .3. For non-displaced individuals, set ˆ (cid:101) Y it − := ˆ Q Y t − | X,D =1 ( ˆ F Y t − | X,D =0 ( Y it − | X i ) | X i )4. Estimate ˆ Q Y t (0) | X,D =1 ( τ ) by quantile regression of ∆ Y it + ˆ (cid:101) Y it − on X i using non-displaced individuals5. For displaced individuals, set ˆ Y it (0) := ˆ Q Y t (0) | X,D =1 ( ˆ F Y t − | X,D =1 ( Y it − | X i ) | X i )Algorithm 1 estimates Y it (0) for all individuals in the treated group. Thus, we canimmediately obtain features of the unconditional distribution of ( Y t (1) , Y t (0) | D = 1) usingthe draws of ( Y it , ˆ Y it (0)) for displaced workers. For example, we can estimate the fraction ofindividuals that have higher earnings following job displacement by1 n (cid:88) i ∈D { Y it − ˆ Y it (0) > } where n denotes the number of displaced workers and D denotes the set of displaced workers.We are also interested in how features of the distribution of Y it (1) − Y it (0) vary with covariates.It is straightforward to run OLS regressions of Y it (1) − ˆ Y it (0) on covariates. These results areinteresting, and we report them in the application. However, our identification results allowus to go substantially further than this. In particular, we can also estimate how covariatesaffect the entire distribution of the effect of job displacement. To estimate this, we againcan use quantile regression. In particular, we suppose that Q ( Y t (1) − Y t (0)) | X,D =1 ( τ | x ) = P ∆ X ( x ) (cid:48) β ∆ X ( τ )where P ∆ X denotes transformations of the covariates. The estimates of these conditionalquantiles and quantile regression parameters are of interest. For example, if we set τ to besmall (e.g., 0.05), β ∆ X ( τ ) provides the effect of covariates on the individual-level effect of jobdisplacement for individuals who are most negatively affected by job displacement.Finally, we are interested in features of the distribution of Y it (1) − Y it (0) across differentvalues of Y it (0); that is, how the effect of job displacement changes across different values ofwhat a displaced worker’s earnings would have been if they had not been displaced. Onceagain, one can estimate OLS regressions of Y it (1) − ˆ Y it (0) on ˆ Y it (0); however, we also use13uantile regression to study how the entire distribution of the effect of job displacement isrelated to non-displaced potential earnings. Here we suppose that Q ( Y t (1) − Y t (0)) | Y t (0) ,D =1 ( τ | y ) = P ∆ Y ( y ) (cid:48) β ∆ Y ( τ )where P ∆ Y ( y ) are transformations of non-displaced potential earnings, and β ∆ Y gives theeffect of non-displaced potential earnings on particular quantiles of the individual-level effectof job displacement.In order to conduct inference, we use the bootstrap. For each of the parameters thatwe consider, we re-sample the original data a large number of times and, at each iteration,re-estimate that parameter using the full estimation procedure. This approach accountsfor estimation uncertainty coming from both the first and second steps of our estimationprocedure. We use data from the Displaced Workers Survey (DWS). The DWS has been administratedevery two years since 1984 as a supplement to the Current Population Survey (CPS) (Flood,King, Ruggles, and Warren (2017)) and contains information on earnings and employmentstatus for displaced workers. Respondents are asked whether they lost their jobs at anypoint in the last three years due to: (i) plant closing or moving, (ii) insufficient work, or (iii)position being abolished. These are sometimes referred to as the “big three” reasons for jobdisplacement (Farber (2017)). Our main results below focus on 2015-2016. We also providesimilar results for 2009-2010 (during the Great Recession) and 1997-1998 (an earlier periodwhen the U.S. economy was quite strong).Although the DWS provides useful information on job displacement status and the cur-rent weekly earnings of displaced workers and their weekly earnings on their lost job, itdoes not provide any information about the earnings of non-displaced workers (though non-displaced workers can be identified). After identifying non-displaced workers using the DWS,we obtain their earnings by matching the DWS to CPS outgoing rotation group data usingindividual-level identification numbers which are available from IPUMS. This matchingprocess helps us to find information on the current weekly earnings as well as weekly earn- Households in the CPS are usually interviewed for four consecutive months, are out of the sample for thenext eight months, and then interviewed for another four months. After the eighth time participating, theyleave the sample. Households that are interviewed in the fourth or eighth month (which are called outgoingrotation groups) are asked additional labor market questions. Thus, using our approach, we observe earningsfor the untreated group in two consecutive years, but they can be different months for different individuals.
Earnings
Covariates
Male 0.57 0.51 0.057 0.00White 0.81 0.82 -0.008 0.48Married 0.51 0.63 -0.113 0.00College 0.33 0.40 -0.066 0.00Less HS 0.07 0.06 0.009 0.21Age 42.11 45.4 -3.294 0.00N 1633 3915
Sources: CPS and Displaced Workers Survey ings in the previous year for non-displaced workers. Effectively, this turns our untreatedgroup into a two period panel dataset. We also drop all non-displaced workers whose earn-ings are missing in either period. For workers that are displaced, we drop those that arenot currently in the labor force and assign 0 earnings to those in the labor force but whoare not currently employed. The timing for available earnings is also somewhat different fordisplaced and non-displaced workers. For displaced workers, the DWS asks for their earningsin their pre-displacement job. But displacement could have occurred any time in the lastthree years. On the other hand, for non-displaced workers, we only have their current weeklyearnings and their earnings one year ago.The summary statistics for key variables of displaced and non-displaced workers in 2016are presented in Table 1. Weekly earnings are about $74 dollars higher for non-displacedworkers than displaced workers in the period before they are displaced. Following job dis-placement, this gap in average weekly earnings increases to $313. This occurs due to acombination of average weekly earnings increasing by $44 for non-displaced workers and de-creasing by $195 for displaced workers (on top of the existing gap in the previous period).For covariates, we include an individual’s sex, race, marital status, age, and education. Dis-placed workers are more likely to be male, not married, younger, and not have a collegedegree; both groups are roughly equally likely to be white or have less than a high schooleducation. 15igure 1: Distributions of Earnings
Notes:
The left panel contains plots of the distributions of earnings in 2015 and 2016 for displacedand non-displaced workers. The right panel plots the distribution of the change in weekly earningsover time separately for displaced and non-displaced workers.
As a first step, Figure 1 plots the distributions of weekly earnings for displaced workers pre-and post-displacement. Clearly, the distribution of post-displacement earnings is shiftedto the left. Notably, there is also a mass point in the distribution of post-displacementearnings – about 20% of displaced workers have 0 earnings. These distributions also exhibita pattern that is consistent with very heterogeneous effects – namely, the difference betweenthe distributions is largest in the lower part of the earnings distributions. This panel alsoplots the distributions of earnings for non-displaced workers in both periods. In the firstperiod, non-displaced workers earn more than displaced workers. And, unlike displacedworkers, in the second time period, the distribution of earnings shifts somewhat to the right(indicating somewhat higher earnings).The right panel of Figure 1 plots the distribution of the change in weekly earnings overtime for displaced workers. Recall that this distribution does not require any identifyingassumption; it is just the difference in earnings over time. Interestingly, our estimates in thefigure indicate that about 37% of displaced workers have higher weekly earnings than theyhad before they were displaced. This number may overstate how many workers actually havehigher earnings than they would have had if they had not been displaced especially in thecase where earnings would have increased in the absence of job displacement. On the otherhand, around 22% of workers earn at least $500 less per week than before displacementand about 10% earn at least $1000 less per week than before displacement – these aresubstantial differences. Thus, it is immediately clear that the difference in the average16igure 2: Counterfactual Distribution of Earnings for Displaced Workers
Notes:
Plots of the actual and counterfactual distribution of earnings for displaced workers. Thecounterfactual distribution also includes a 95% pointwise confidence interval computed using theempirical bootstrap with 1000 iterations. decrease in earnings for displaced workers relative to non-displaced workers of $239 per week(see Table 1) masks substantial heterogeneity. The right panel also displays the distributionof the change in earnings over time for non-displaced workers. This distribution is notablydifferent with non-displaced workers being much less likely to experience large declines intheir earnings over time and more likely to experience an increase in earnings over time.The next step in our analysis is to construct the counterfactual distribution of weeklyearnings that displaced workers would have experienced if they had not been displaced fromtheir jobs. We do this using the approach of Callaway, Li, and Oka (2018) as describedin Equation (1) and Algorithm 1. Figure 2 plots this counterfactual distribution. Noticethat the counterfactual distribution sits to the right of the actual distribution of earnings.Also, the biggest difference between the two distributions occurs in the lower part of thedistribution. Once the counterfactual distribution is identified, this also implies that theaverage effect of job displacement is identified. We estimate that job displacement reduces The distribution depends on the value of the covariates; the figure reports the average of the distributionover all values of covariates for displaced workers in the dataset. This is a standard way of convertingconditional effects into unconditional effects.
Notes:
The red line is the estimated distribution of the effect of job displacement for displacedworkers as discussed in the text. The shaded gray area provides a uniform 95% confidence bandcomputed using the empirical bootstrap with 1000 observations. earnings by $157 per week on average, which is about 18% of pre-displacement earnings.
Remark 3.
The results in Figure 2 are also closely related to quantile treatment effects. TheQuantile Treatment Effect on the Treated (QTT) is the difference between the quantiles ofobserved outcomes for displaced workers and the quantiles of the counterfactual distributionof outcomes that they would have experienced if they had not been displaced. The QTTcomes from inverting the distributions in Figure 2. Because the difference between thesetwo distributions is largest at the lower part of the distribution, it is tempting to interpretthis as saying that the effect of job displacement is largest for workers in the lower partof the earnings distribution. This is an incorrect interpretation though because it ignoresthe possibility that workers change their ranks in the distribution of earnings due to jobdisplacement (e.g., workers who would have had high earnings if they had not been displacedremaining unemployed following displacement). In fact, we find evidence (discussed below)that points in exactly the opposite direction – that the effect of job displacement appears tobe larger for high earnings workers than low earnings workers.Next, we can map each value of Y it (1) to ˆ Y it (0) and create a pair of ( Y it (1) , ˆ Y it (0)) for each18isplaced worker. Figure 3 plots the distribution of Y it (1) − ˆ Y it (0) for displaced workers. Thisis the distribution of the difference between earnings for displaced workers relative to whatthey would have earned if they had not been displaced and maintained the same rank in theearnings distribution over time. Under the additional assumption of rank invariance overtime, this is the distribution of the effect of job displacement. Interestingly, this distributionis remarkably close to the distribution of the change in outcomes over time (as in the rightpanel of Figure 1). This implies that our results for the distribution of the actual effectof job displacement are very similar to our earlier estimates that instead use the change inearnings over time for displaced workers. Here, we estimate that (i) 42% of displaced workershave higher earnings following displacement than they would have had if they had not beendisplaced and maintained the same rank in the earnings distribution over time, (ii) 21%have at least $500 less in weekly earnings than they would have had if they had not beendisplaced and maintained the same rank in the earnings distribution over time, and (iii) 8%have at least $1000 less weekly earnings than they would have had if they had not beendisplaced and maintained the same rank in the earnings distribution over time.Taken together, our results so far indicate that there is substantial heterogeneity in theeffect of job displacement. Even though there is a fairly large average effect of job displace-ment, a substantial fraction of workers appear to be no worse off due to job displacementthan they would have been if they had not been displaced. On the other hand, the nega-tive effects of job displacement seem to be largely concentrated among 10-20% of displaced It is worth explaining more why the distributions are so similar. The change in earnings over time isgiven Y it − Y it − for displaced workers. The estimates in Figure 3 come from the distribution of Y it − ˆ Y it (0) fordisplaced workers. Thus, any differences between the two distributions comes from differences between Y it − and Y it (0). From Equation (2), we generate Y it (0) = Q Y t (0) | X,D =1 ( F Y t − | X,D =1 ( Y it − | X i ) | X i ); in practice,this amounts to finding an individuals rank in the conditional distribution of outcomes in time period t − Y it − = Q Y t − | X,D =1 ( F Y t − | X,D =1 ( Y it − | X i ) | X i ); in other words, an alternative way to obtain an individual’soutcome in period t − t − t − Y it − Y it − and Y it − Y it (0) for displaced workers comes down to differences in the conditional quantiles (ordistributions) of Y it (0) and Y it − . In our case, these two distributions are very similar – suggestive evidenceof this can be found in Figures 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 earningsfollowing 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 ourcase 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 bereluctant to leave it for the possibility of a higher paying job when they have less information about otheraspects 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 theseresults even under conservative assumptions on measurement error in earnings.
Notes:
QR estimates of the effect of covariates on the quantiles of the effect of job displacement. Thesolid red horizontal lines provide OLS estimates of the effect of each covariate, and the horizontaldashed line contains a 90% confidence interval. The other multi-colored lines provide QR estimatesof the effect of each covariate at particular quantiles from 0.1, 0.2, . . . , 0.9. The shaded areacontains pointwise 90% confidence intervals from the quantile regressions. workers who experience large negative effects.Next, we use quantile regression to see how covariates affect the distribution of thedifference between earnings following displacement for displaced workers and what theywould have been in the absence of displacement and if workers had maintained their rankin the earnings distribution over time. Figure 4 provides estimates of the effect of eachcovariate across different quantiles of this conditional distribution. There are some quiteinteresting patterns here. On average, the effect of job displacement is somewhat morenegative for men than for women, but the effect is very heterogeneous. For individuals thatexperience large negative effects, the effects for men are much more negative than the effects20or women. On the other hand, for individuals that are towards the top of the distributionof the treatment effect (i.e., experience small or positive effects of job displacement), mentend to have larger benefits than women. Differences in the effect of job displacement byrace tend to be small and not exhibit strong patterns at different parts of the conditionaldistribution. The effect of job displacement for college graduates is also very heterogeneous.Some college graduates experience very large negative effects from job displacement, whilecollege graduates (conditional on doing well following job displacement) tend to do betterthan high school graduates. For individuals with less than a high school education, theseresults are almost exactly reversed. Finally, our results indicate that being older increasesthe negative effects of job displacement on average. Once again, though, the effects are quiteheterogeneous – among workers who are most negatively affected by job displacement, beingolder has an especially large negative effect.These results suggest that the largest negative effects of job displacement tend to be forolder, male, college graduates. This should probably not be a surprising result as the effectof job displacement depends on both earnings following job displacement, Y it (1), as wellas what earnings would have been in the absence of job displacement, Y it (0). Older, male,college graduates may have large earnings losses due to job displacement particularly in thecase where if, had they not been displaced, they would have had high earnings.Finally, in this section, we investigate how the effect of job displacement varies with Y t (0) – i.e., how the effect varies across individuals as a function of what their earningswould have been if they had not been displaced. We plot quantile regression estimates fromregressing ( Y it (1) − ˆ Y it (0)) on ˆ Y it (0) in Figure 5. On average, the effect of job displacementis larger for individuals who would have had higher earnings if they had not been displacedfrom their job and had maintained the same rank in the earnings distribution over time.Notably, this is exactly the opposite interpretation as one would be tempted to make if oneonly compared the marginal distributions (see discussion in Remark 3). In addition, there issubstantial heterogeneity. For individuals that experience the largest negative effects of jobdisplacement, these negative effects appear to be substantially larger for those who wouldhave had high earnings if they had not been displaced and maintained their rank. On theother hand, for those who are less affected by job displacement, the difference between theeffect for those who would have had high earnings relative to those who would have had lowearnings in the absence of job displacement is small. Recall that the outcome in these quantile regressions is Y it (1) − ˆ Y it (0) for displaced individuals. Thismeans that “large negative effects” occur at the lower quantiles in Figure 4. Y t (0) Notes:
QR estimates of the effect of what earnings would have been in the absence of job displace-ment, Y t (0), on the quantiles of the effect of job displacement as discussed in the text. The solidhorizontal line provides OLS estimates of the effect of non-displaced potential earnings, and thehorizontal dashed line contains a 90% confidence interval. The other line provides QR estimatesof the effect of non-displaced potential earnings at particular quantiles from 0.1, 0.2, . . . , 0.9. Theshaded area contains pointwise 90% confidence intervals from the quantile regressions computedusing the bootstrap with 1000 iterations. Next, we provide analogous results for 2009-2010 (corresponding to the Great Recession)and for 1997-1998 (an earlier time period when the U.S. economy was quite strong). Webriefly discuss the main results from these other periods below and provide additional detailsin the appendix (in particular, there we provide summary statistics and quantile regressionestimates of the effect of covariates and the effect of non-displaced potential earnings on thedistribution of the effect of job displacement). All of the results in this section use the sameidentification arguments and estimation approaches that were applied to the 2015-2016 dataabove.
Results for 2009-2010
These results are for workers who were displaced at the height of the Great Recession.22igure 6: Main Results for 2009-2010
Notes:
The left panel contains plots of the distributions of earnings for displaced workers as wellas their counterfactual distribution of earnings if they had not been displaced. The right panelcontains the distribution of the effect of job displacement for displaced workers as discussed in thetext.
Figure 6 plots the observed and counterfactual distributions of outcomes for displaced work-ers. The effects of job displacement are much larger, on average, than in 2015-2016. Weestimate that workers who were displaced from their job earn $308 less on average than theywould have earned if they had not been displaced; this corresponds to 39% lower earningson average relative to pre-displacement earnings. Much of these effects appear to be drivenby not being able to find work. 41% of displaced workers continued to be unemployed in2010 (for 2015-2016, only 20% of displaced workers continued to be unemployed in 2016).Interestingly, we estimate that 28% of displaced workers have higher earnings than theywould have had if they had not been displaced and maintained their rank in the earningsdistribution over time. Even when we just compare current earnings to pre-displacementearnings, we find that 21% of displaced workers had higher earnings following displacementthan they had in their pre-displacement job. This indicates that even though the effects ofjob displacement appear to be substantially larger during the Great Recession, there is stillsubstantial heterogeneity and a non-trivial fraction of displaced workers seem to have higherearnings than they otherwise would have had.The effect of covariates on the distribution of the effect of job displacement in 2009-2010is broadly similar to the effect in 2015-2016 (see Figure 11 in the appendix). In particular,among those who appear to be most negatively affected by job displacement, older, male,college graduates tend to be the most affected (here, there is also some evidence that amongthose most affected by job displacement, married displaced workers are also more negatively23ffected by job displacement). Finally, similarly to 2015-2016, the effect of job displacementtends to be negatively related to earnings that individuals would have experienced if theyhad not been displaced (see Figure 12 in the appendix). These effects tend to be biggest forindividuals who experience the largest negative effects of job displacement.
Results for 1997-1998
Finally, we examine the effect of job displacement in 1997-1998. This is an earlier periodthan the ones we have considered so far, and the U.S. economy was quite strong during thisperiod. Figure 7 contains our main estimates from this period. We estimate that displacedworkers earned on average $68 less per week than they would have earned if they had notbeen displaced. This estimate corresponds to 13% lower earnings on average relative to pre-displacement earnings. This estimate is somewhat smaller than the corresponding estimatefor 2015-2016 and much smaller than the corresponding estimate for 2009-2010. Part of thereason for the smaller effects here is that only 14% of displaced workers are unemployed in1998. In addition, we estimate that 45% of displaced workers have higher earnings than theywould have had if they had not been displaced and maintained their rank in the earningsdistribution over time. Similarly, 42% of displaced workers had higher earnings in theircurrent job than they did in their pre-displacement job. Finally, our estimates for the effectof covariates and untreated potential outcomes are broadly the same as in the other periods(see Figures 13 and 14 in the appendix). For displaced workers that are most affected by jobdisplacement, these effects once again tend to be largest for older, male, college graduatesand for those who would have had high earnings if they had not been displaced. Givenour results in earlier sections, these results seem to indicate that the finding that the largesteffects of job displacement are concentrated among these groups is robust across time periodsand across various states of the macroeconomy.24igure 7: Main Results for 1997-1998
Notes:
The left panel contains plots of the distributions of earnings for displaced workers as wellas their counterfactual distribution of earnings if they had not been displaced. The right panelcontains the distribution of the effect of job displacement for displaced workers as discussed in thetext.
To conclude this section, we discuss a number of additional robustness checks: (i) usingChange in Changes as a replacement first step estimator, (ii) placebo tests related to ourresults on treatment effect heterogeneity, (iii) placebo tests related to regression towardsmean earnings over time, and (iv) specification tests for our linear QR specifications. In thissection, for brevity, we discuss only the results for 2016.
Change in Changes
As discussed above, using Change in Changes (Athey and Imbens (2006) and Melly andSantangelo (2015)) provides a reasonable alternative to our approach. Change in Changesimmediately recovers F Y t (0) | X,D =1 as in Step 1 of our identification argument. Then, thesame arguments as in our Step 2 immediately apply. Panel (a) of Figure 8 provides ouroriginal estimate of the counterfactual distribution along with the corresponding estimatewhen Change in Changes is used in the first-step instead. These results are very similar.Likewise, Panel (b) of Figure 8 plots estimates of the distribution of the effect of job dis-placement in both of these cases. These results are also quite similar; the results coming For the distribution of the effect of job displacement, there are some places where the estimate of thisdistribution using Change in Changes does fall outside of the 95% uniform confidence band using our originalapproach. However, despite the uniform confidence bands, the figure does not provide a formal test that thedistributions are equal because it does not account for sampling uncertainty using Change in Changes. (a) Counterfactual Distributions (b) Distribution of the Effect of Job Displacement
Notes:
Panel (a) contains our original estimates of the counterfactual distribution of earnings thatdisplaced workers would have experienced if they had not been displaced (which are available as theblue line along with a 95% uniform confidence band) to the same counterfactual distribution thatarises when Change in Changes is used as an alternative first-step estimator. Panel (b) containsour original estimates of the distribution of the effect of job displacement (which are available asthe blue line along with a 95% uniform confidence band) along with estimates of the distributionof the effect of job displacement arising from using Change in Changes as an alternative first-stepestimator. The results in this figure are for 2016. from Change in Changes generally indicate a somewhat more negative effect of job displace-ment. On average, we originally estimate that displaced workers lose $157 per week relativeto what they would have earned if they had not been displaced; using Change in Changes,we estimate that they would have lost $227 per week. We originally estimate that workers inthe 10th percentile of the effect of job displacement (these are among those most negativelyaffected by job displacement) lose $881 per week; using Change in Changes, we estimatethat they lose $957 per week. For workers in the 90th percentile of the effect of job displace-ment, we originally estimate that their earnings increase by $436 per week; using Change inChanges, we estimate that they earn $347 more.
Placebo Tests for Treatment Effect Heterogeneity
Our main results on treatment effect heterogeneity rely heavily on rank invariance as inAssumption 5. Recall that, under our other identifying assumptions, for displaced workers,we identify ˜ Y it (0) – this is the outcome individual i would experience if they had not beendisplaced and had the same rank in the earnings distribution as in the previous period.Rank invariance additionally implies that Y it (0) = ˜ Y it (0). It is possible that treatment effectheterogeneity could arise spuriously due to violations of rank invariance. To see this, consider26he case where there is no effect of job displacement on earnings so that Y it (1) = Y it (0) forall individuals. Even in this case, if rank invariance does not hold, then our approach wouldstill detect some heterogeneous effects of job displacement (since Y it (1) (cid:54) = ˜ Y it (0)).Next, we discuss several ways to detect if there appears to be meaningful heterogeneityapart from rank invariance. First, we compute Spearman’s Rho (the rank correlation) for Y t and Y t − for both the group of displaced and non-displaced workers. Rank invariance holdsif Spearman’s Rho is equal to 1. For non-displaced workers, Spearman’s Rho is equal to 0.69.This is strong positive dependence but, since it is less than 1, it essentially implies that rankinvariance does not hold for non-displaced workers. One way to check if there is meaningfulheterogeneity is to compare Spearman’s Rho for displaced and non-displaced workers. If thecorrelation of ranks of earnings is similar for displaced workers and non-displaced workers,this would be a piece of evidence against meaningful heterogeneity due to job displacement.Instead, for displaced workers, Spearman’s Rho is 0.44. This is substantially lower; it meansthat displaced workers ranks in the earnings distribution are less correlated over time thannon-displaced workers. And it is suggestive evidence that there is additional heterogeneitybeyond that mechanically introduced by violations of rank invariance.Second, we propose to impute Y it (0) for non-displaced individuals under the assumptionof rank invariance; in particular, we impute ¨ Y it (0) := Q Y t | X,D =0 ( F Y t − | X,D =0 ( Y it − )) whichis the earnings of non-displaced individual i in the second time period if they maintainedtheir rank from the first period. If rank invariance holds for the group of non-displacedworkers, then Y it (0) (which is observed for non-displaced workers) should be equal to ¨ Y it (0).We compute the standard deviation of Y it (1) − ˆ Y it (0) for the group of displaced workers and Y t (0) − ˆ¨ Y it (0) for the group of non-displaced workers (where ˆ¨ Y it (0) is a non-displaced workersearnings imputed as above with conditional distributions/quantiles estimated by quantileregression). For non-displaced workers, the standard deviation is $515, and for displacedworkers, the standard deviation is $617 – once again suggesting that there is some additionalheterogeneity due to job displacement that is not directly coming from the assumption ofrank invariance.Finally, we plot the distribution of | Y it (1) − ˆ Y it (0) − ˆ µ | (where ˆ µ is the average differencebetween Y it (1) and ˆ Y it (0)) for the group of displaced workers as well as the analogous distri-bution of placebo effects for the group of non-displaced workers. These results are providedin Figure 9 and are similar to the previous ones – there appears to be more treatment effectheterogeneity for displaced workers than what arises for non-displaced workers when imput-ing their earnings under rank invariance. Taken together, these results suggest that, while This does imply that unconditional rank invariance does not hold here, but our assumptions have beenabout conditional rank invariance which is somewhat weaker.
Notes:
Plots of treatment effect heterogeneity under rank invariance for the group of displacedworkers (blue line) and placebo treatment effect heterogeneity under rank invariance for the groupof non-displaced workers (red line) as discussed in the text. our results can partially be explained by “spurious” heterogeneity arising from violations ofthe assumption of rank invariance, there still appears to be meaningful heterogeneity apartfrom rank invariance.
Placebo Tests for Regression to the Mean
Another of our main results was that the effect of job displacement was larger for individualswho would have had higher earnings in the absence of job displacement relative to individualsthat would have had lower earnings (see Figure 5 and related discussion). This result alsorelied on the rank invariance condition in Assumption 5. An alternative explanation forthis sort of result is that there is regression to the mean – i.e., that individuals with higherearnings would have tended to experience relative decreases in their earnings even in theabsence of job displacement. Regression to the mean implies a particular violation of rankinvariance that could potentially lead to results that look like those in Figure 5 even ifthe effect of job displacement does not systematically vary with earnings in the absence ofdisplacement.For example, suppose that the effect of job displacement is constant, i.e., Y it (1) − Y it (0) = α for all i . Violations of rank invariance mean that ˜ Y it (0) (cid:54) = Y it (0), but, in addition, regressionto the mean says that Y it (0) will tend to be less than ˜ Y it (0) for large values of ˜ Y it (0) andwill tend to be greater than ˜ Y it (0) for small values of ˜ Y it (0). In other words, imposing rankinvariance in the presence of regression to the mean tends to overstate earnings of high28igure 10: Placebo Tests for Regression to the Mean l l l l l l l l ll l l l l l l l l −1.00−0.75−0.50−0.250.00 0.00 0.25 0.50 0.75 1.00 tau Q R C oe f s llll Avg. Placebo Coef.Original Estimates
Notes:
The red dots are the average quantile regression coefficients on earnings in the absence of jobdisplacement over 1000 placebo estimates using the approach discussed in the text. The confidencebands are the corresponding 95th and 5th percentiles of the quantile regression coefficients. Thered line is the average OLS estimate of the effect of earnings in the absence of job displacement over1000 placebo estimates, and the dotted red lines are the corresponding 95th and 5th percentiles.The blue dots and blue line provide our original corresponding estimates of the quantile regressionand OLS estimates. These results are for 2016. earners and understate earnings of low earners (both in the absence of displacement). Thissuggests that regression to the mean could lead to results that are quantitatively similar tothe ones that we report.In order to think about regression to the mean, we once again exploit having access to theuntreated group. Our goal here is to think about whether or not our results on differentialeffects of job displacement by earnings in the absence of displacement can be explainedby regression to the mean of earnings. In order to address this, we take the group of non-displaced workers and randomly assign 1633 (this is the original number of displaced workers)to be treated. We assign the remaining individuals to be untreated. By construction, the“effect” of job displacement should not vary across different values of earnings in the absenceof displacement. We construct this sort of dataset 1000 times and, for each one, we compute the same esti-mates (QR and OLS) of job displacement effects on earnings in the absence of displacement(i.e., we replicate the analysis in Figure 5 but with an adjusted dataset). These results arereported in Figure 10. When we use this approach, we find that placebo-displaced workerstend to experience larger placebo-declines in earnings across higher imputed earnings – this Note that, besides Assumption 5, our other identifying assumptions hold by construction in this setup.
Notes:
Specification tests for the linear quantileregression specifications for Y t − in Assumption 6. Thereported p-value is calculated using 100 bootstrapiterations. is consistent with the idea that, even in the absence of job displacement, there would besome regression to the mean in terms of earnings. That being said, our original estimatesare noticeably larger in magnitude. Together, these results suggest that our original resultsmay be somewhat biased (due to regression to the mean), but that we are still picking upa meaningful pattern that the effects of displacement appear to be larger for higher earningindividuals. Quantile Regression Specification Tests
We have used quantile regression throughout the paper to estimate conditional distributionsand conditional quantiles. As discussed above, using quantile regression in our applicationhas a number of advantages and nicely balances flexibility of the estimator with feasibilityin our setup. That being said, the quantile regression specifications specifications do involveparametric assumptions, and these assumptions are testable. We implemented the specifi-cation test proposed in Rothe and Wied (2013). Here, we focus on testing the specificationsin Assumption 6 only for earnings in period t − We report these results in Table 2. We do notreject the linear quantile regression specification for any of our estimators. These are the quantile regressions that show up in the first step of our estimation procedure. We douse quantile regression in second step estimates, but it is not immediately clear how to adapt the Rothe andWied (2013) test to that case due to there not being an observed distribution that we can directly compareto. Conclusion
In this paper, we have studied how the effect of job displacement varies across differentindividuals. To do this, we compared the earnings of displaced workers to what their earningswould have been if they had maintained their rank in the (conditional) distribution of weeklyearnings (though we allow for the distribution of weekly earnings to change over time). Akey requirement of our approach was to be able to estimate several conditional distributionsin a first step in a way that was both not too restrictive while also being feasible with amoderate sized data set and a fairly large number of covariates. To do this, we relied heavilyon first-step quantile regression estimators.We found that displaced workers lose about $157 per week due to job displacement, onaverage. However, that average effect masks a tremendous amount of heterogeneity. A largefraction of workers appear to be no worse off (or even better off) in terms of their earningsfollowing job displacement than they would have been if they had not been displaced. Onthe other hand, another large fraction loses substantially more than the average earningsloss. Once we had obtained the distribution of the effect of job displacement, we usedquantile regression to study how the distribution of the effect of job displacement dependson covariates. We also showed that this distribution varies substantially across sex, educationlevels, and age, as well as across different amounts of earnings that displaced workers wouldhave had if they had not been displaced. 31 ompliance with Ethical Standards
Conflict of Interest: Afrouz Azadikhah Jahromi declares that she has no conflict of interest.Brantly Callaway declares that he has no conflict of interest.Ethical approval: This article does not contain any studies with human participants oranimals performed by any of the authors.
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Additional Tables and Figures
A.1 2009-2010 Results
Table 3: 2009-2010 Summary StatisticsDisplaced Non-Displaced Difference P-val on Difference
Earnings
Covariates
Male 0.60 0.48 0.122 0.00White 0.83 0.85 -0.017 0.04Married 0.53 0.62 -0.096 0.00College 0.25 0.38 -0.123 0.00Less HS 0.10 0.06 0.044 0.00Age 41.50 44.87 -3.371 0.00N 4088 4000
Sources: CPS and Displaced Workers Survey
Notes:
QR estimates of the effect of covariates on the quantiles of the effect of job displacementin 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 linesprovide 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. Y t (0) Notes:
QR estimates of the effect of what earnings would have been in the absence of job displace-ment, 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 QRestimates 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 regressionscomputed using the bootstrap with 1000 iterations. .2 1997-1998 Results Table 4: 1997-1998 Summary StatisticsDisplaced Non-Displaced Difference P-val on Difference
Earnings
Covariates
Male 0.56 0.50 0.057 0.00White 0.87 0.88 -0.008 0.34Married 0.55 0.66 -0.108 0.00College 0.24 0.31 -0.069 0.00Less HS 0.12 0.08 0.038 0.00Age 38.69 42.03 -3.34 0.00N 2387 3842
Sources: CPS and Displaced Workers Survey
Notes:
QR estimates of the effect of covariates on the quantiles of the effect of job displacementin 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 linesprovide 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. Y t (0) Notes:
QR estimates of the effect of what earnings would have been in the absence of job displace-ment, 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 QRestimates 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 regressionscomputed using the bootstrap with 1000 iterations.(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 QRestimates 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 regressionscomputed using the bootstrap with 1000 iterations.