Long-Term Unemployment and the Great Recession: The Role of Composition, Duration Dependence, and Nonparticipation

We explore the role of composition, duration dependence, and labor force nonparticipation in accounting for the sharp increase in the incidence of long-term unemployment (LTU) during the Great Recession. We show that compositional shifts account for very little of the observed increase in LTU. Using panel data from the Current Population Survey for 2002–7, we calibrate a matching model that allows for duration dependence in unemployment and transitions between employment, unemployment, and nonparticipation. The calibrated model accounts for almost all of the increase in LTU and much of the observed outward shift in the Beveridge curve between 2008 and 2013.


I. Introduction
This paper investigates whether a search and matching model can explain important features of the US labor market in the Great Recession and its aftermath. In particular, we ask whether such a model can account for the rise in the unemployment rate and the increase in the incidence of long-term unemployment among the unemployed. 1 To motivate our analysis, we decompose the overall unemployment rate by unemployment duration. Figure 1 plots the unemployment rate We begin our analysis by showing that between 2008 and 2013, compositional shifts toward groups with traditionally longer unemployment durations account for very little of the overall rise in the incidence of longterm unemployment documented in figure 2. We show that long-term unemployment increased for virtually all groups and that compositional shifts do not go very far in accounting for the rise in long-term unemployment. For this exercise, compositional shifts refer to the changes in observed characteristics of unemployed workers-specifically, variables in the Current Population Survey ðCPSÞ related to demographics, occupation, industry, region, and the reason for unemployment. We emphasize that this analysis cannot account for changes in the composition of the unemployed based on unobserved characteristics.
We next examine the extent to which a matching model along the lines of Mortensen and Pissarides ð1994Þ and Shimer ð2005Þ can account for the observed increase in long-term unemployment and the observed shift in the Beveridge curve. To do this, we enrich a standard matching model along three dimensions. First, we allow for duration dependence in the job finding rate of the unemployed. Second, we allow for flows between employment ðEÞ, unemployment ðUÞ, and nonparticipation ðNÞ, instead of focusing exclusively on flows between E and U, as in a standard match- ing model. Third, we allow flows from employment and nonparticipation into unemployment to occur not just into short durations but also into long unemployment durations, consistent with observed flows in the CPS.
Our rationale for exploring duration dependence in the unemployed job finding rate is based on several recent résumé audit studies that show that callbacks from employers to set up an interview decline with the current nonemployment duration on a job applicant's resume ðGhayad 2013; Kroft, Lange, and Notowidigdo 2013;Eriksson and Rooth 2014Þ. This form of employer discrimination could arise from human capital depreciation or employer screening, whereby employers perceive the longterm unemployed to be less productive employees. Negative duration de- FIG. 2.-Long-term unemployment and the Beveridge Curve. This figure uses data from the Current Population Survey and the Job Openings and Labor Turnover Survey. Panel A shows the share of unemployed workers aged 25-55 who have unemployment durations of more than 26 weeks. The pooled, cross-sectional data come from monthly CPS surveys. In this panel and in figures 3-5, month fixed effects have been residualized out of the data to account for seasonality, and the data are smoothed by taking a 3-month average around each observation. Panel B shows the Beveridge curve, the relationship between unemployment and vacancies, with both series normalized by the total population ði.e., labor force plus non-participantsÞ. The arrow in panel B indicates the apparently outward movement of the Beveridge curve after 2008. A color version of this figure is available online. pendence in the job finding rate could also be due to lower search effort among the unemployed at longer durations due to discouragement.
Negative duration dependence in the exit rate from unemployment can potentially "amplify" the effects of a downturn in the labor market and increase long-term unemployment. According to a recent report by the Congressional Budget Office, long-term unemployment may "produce a self-perpetuating cycle wherein protracted spells of unemployment heighten employers' reluctance to hire those individuals, which in turn leads to even longer spells of joblessness" ðCongressional Budget Office 2012Þ. As a result, negative duration dependence in the job finding rate from unemployment would appear to be a promising candidate explanation for understanding the recent sharp rise increase in long-term unemployment. As more workers are pushed into longer unemployment spells, negative duration dependence lowers the average job finding rate and thus increases the overall unemployment rate. Therefore, duration dependence can potentially explain both the rise in long-term unemployment as well as the observed outward shift in the Beveridge curve during the Great Recession, as documented in Elsby, Hobijn, and Sahin ð2010Þ. Our rationale for exploring the nonparticipation margin is motivated by previous work demonstrating the fluid boundary between nonparticipation and unemployment ðClark and Summers 1979; Flinn and Heckman 1983;Card and Riddell 1993;Jones and Riddell 1999;Elsby, Hobijn, Fig. 2 (Continued ) and Sahin 2015Þ, as well as recent research on the effects of unemployment insurance ðUIÞ benefit extensions on transitions between unemployment, employment, and nonparticipation ðRothstein 2011; Farber and Valetta 2013Þ. The recent UI research finds significant effects of extended UI in reducing the exit rate from unemployment to nonparticipation. The substantial UI benefit extensions during the Great Recession may therefore have induced some jobless individuals to continue to report themselves as unemployed in the CPS, contributing to the observed rise in long-term unemployment. Beyond this specific mechanism, we also observe large changes in transition rates to and from nonparticipation since 2008.
We calibrate our enriched matching model using monthly data in the years before the Great Recession ð2002-7Þ and study how well the calibrated model fits the data during the Great Recession, holding fixed the calibrated parameters. 2 In our analysis, we implement a two-step empirical approach. In the first step, we measure transition rates between the different labor market states ðE, U, and NÞ over the entire 2002-13 period and estimate duration dependence using data from 2002 to 2007. In the second step, we calibrate the matching model parameters. By first measuring transition rates without imposing the structure of the matching model, we obtain measured hazard rates ðbetween unemployment, employment, and nonparticipationÞ that are robust to model misspecification. 3 An alternative to our two-step approach would be to estimate the hazard rates and the matching model parameters jointly in a single step. One advantage of our two-step approach is that it clarifies when failures to match the evolution of the job finding rates over this time period are due to shortcomings in the enriched matching model. Another advantage is that it is straightforward to impose alternative assumptions about the magnitude of "true" duration dependence to explore the sensitivity of the results ðsince the second step takes the duration dependence estimates from the first step as given, allowing alternative duration dependence estimates to be "plugged in" at the second stageÞ.
In all of our analyses, we treat vacancies, transitions from employment to unemployment and nonparticipation, and transitions between nonparticipation and unemployment as the exogenous "forcing variables" of the model. By contrast, we allow the job finding rates ðfor both the unemployed and nonparticipantsÞ, the labor market states, and the distribution of unemployment durations to all evolve endogenously ðholding constant the calibrated parameters from the 2002-7 periodÞ. Clearly, a more complete model of the economy would endogenize the forcing variables. However, we treat these variables as exogenous because endogenizing them would require a model of vacancy creation as well as a model of labor demand, which is beyond the scope of this paper. In our sensitivity analysis, we manipulate the vacancy rates that we use in our counterfactual experiments to examine how the model performs when the strength of labor demand changes. 4 Summarizing our results, we find that our calibrated model does a very good job of accounting for the increase in the incidence of long-term unemployment and can also account for much of the observed outward shift in the Beveridge curve. These conclusions are fairly robust to a variety of alternative assumptions, such as allowing duration dependence to vary over the business cycle, as suggested by the experimental results in Kroft et al. ð2013Þ. On the other hand, our model has difficulty matching the observed relationship between vacancies and nonparticipation during the Great Recession. In particular, it predicts a job finding rate for nonparticipants that is too high after 2008. Why N-to-E transitions fell so much more than expected ðand continue to remain so low through 2013Þ therefore remains an important open question for future work.
To understand the relative importance of duration dependence and changes in ðN-to-U, U-to-N, and E-to-NÞ transition rates in the model's ability to account for the observed increase in long-term unemployment and the observed outward shift in the Beveridge curve, we simulate the calibrated model "shutting down" each of these features one by one. First, we shut down duration dependence by recalibrating the model under the assumption that the job finding rate is independent of unemployment duration. In this scenario, we find that the model accounts for much less of the rise in long-term unemployment and the observed outward shift in the Beveridge curve. We interpret this as evidence that duration dependence plays an important role in accounting for both of these phenomena.
Second, we shut down the exogenous nonparticipation flows by fixing these flows at the values observed at the end of 2007, and we find that the predicted long-term unemployment shares and unemployment rates both deviate substantially from our baseline calibrations. In particular, the counterfactual predictions show much less of an outward shift in the Beveridge curve. The E-to-N flows are not central to this result, but Uto-N flows and particularly N-to-U flows play an important role. This closely relates to results in Elsby et al. ð2015Þ, which find that the flows from unemployment to nonparticipation explain close to one-third of the cyclical variation in the unemployment rate. Overall, our analysis sug-gests that changes in the flows from nonparticipation to unemployment ðspecifically, flows into long-term unemploymentÞ play an important role in the increase of long-term unemployment after 2008.
One explanation for this finding centers around the very large UI extensions that took place during the Great Recession. Our results indicate that flows from unemployment to nonparticipation declined from about 20% monthly in 2008 to about 14% monthly in 2009 and only slowly recovered after 2009. We conjecture that many unemployed individuals may have remained in unemployment longer and are now classified as long-term unemployed ðrather than being classified as nonparticipantsÞ. We also speculate that UI extensions may have played a role in causing many UI recipients to continue to consider themselves as labor force participants, even after many weeks of joblessness. This is consistent with the empirical findings of Rothstein ð2011Þ and Farber and Valletta ð2013Þ. Our counterfactual estimates suggest that a large amount of the increase in unemployment with durations longer than 52 weeks might be attributable to the decline in the rate at which the unemployed became nonparticipants. While our calibrated model can account for much of the outward shift in the Beveridge curve, it does not provide a complete accounting of the shift. Davis, Faberman, and Haltiwanger ð2013Þ offer a promising explanation for the residual shift in the Beveridge curve not accounted for by our matching model, which focuses on the vacancy rate rather than the unemployment rate in the Beveridge curve. They find a reduction in "recruiting intensity" and in "effective vacancies," which may indicate continuing weak labor demand since the Great Recession. According to their research, employers are listing vacancies but are not recruiting workers as intensively to fill them ðas in the recent pastÞ, implicitly waiting around for the "perfect" job candidates.
Our work closely relates to Elsby et al. ð2011Þ, which provides a thorough empirical exploration of long-term unemployment and nonparticipation in the Great Recession. An important difference is that our analysis is primarily based on a quantitative exploration of a calibrated matching model. One advantage of our model-based approach is that we can more readily conduct counterfactual scenarios to assess the relative importance of duration dependence and nonparticipation in accounting for the observed increase in long-term unemployment and the observed outward shift of the Beveridge curve. Our paper is also similar to subsequent research by Krueger, Cramer, and Cho ð2014Þ, who build on and extend our matching function to allow for differential effects by unemployment duration within the matching function and also allow for differential labor force withdrawal ði.e., U-to-N transitionsÞ for the short-term and longterm unemployed. They also evaluate whether the long-term unemployed exert differential pressure on wage growth and inflation than the shortterm unemployed.
Our work also relates to Barnichon and Figura ð2015Þ, which estimates a standard matching function over the period 1967-2012 and finds that the predicted job finding rate is much lower than the observed job finding rate during the Great Recession. Barnichon and Figura consider a generalized matching function incorporating worker heterogeneity ðdemographics, reason for unemployment, and duration of unemploymentÞ and labor market segmentation ðgeography and occupation groupÞ and find that it matches observed job finding rates during the Great Recession much more closely. While they consider a two-state model of the labor market and focus primarily on job finding rates, our paper considers a three-state model, adding nonparticipation, and also focuses more on the incidence of long-term unemployment.
Finally, our paper is broadly related to an active literature in macroeconomics on the relative contributions of inflows into and outflows from unemployment to unemployment dynamics ðHall 2005; Elsby, Michaels, and Solon 2009;Fujita and Ramey 2009;Barnichon 2012;Shimer 2012;Elsby et al. 2015Þ. The emerging consensus from this literature is that the outflow contribution is at least 50%, but the literature is agnostic as to the factors behind falling outflows from unemployment. Our paper contributes to this literature by explicitly investigating two specific mechanisms behind the fall in the outflow rate: duration dependence and transitions in and out of the labor force. 5 The remainder of the paper proceeds as follows. Section II describes the data. Section III investigates the role of composition. Section IV describes the matching function that we use to investigate the role of duration dependence and nonparticipation. Section V describes the methodology for the model calibration. Section VI presents the results of the model calibration. Section VII reports the counterfactual scenarios and discusses alternative explanations. Section VIII concludes.

II. Data
This section briefly describes our data sources. Appendix A provides more detail on the data used in our analysis. 5 A related paper that takes into account negative duration dependence in job finding rates is Hornstein ð2012Þ. Hornstein extends the framework in Shimer ð2012Þ to allow for two types of unemployed workers: those with high exit rates from unemployment ðthe short-term unemployedÞ and those with low exit rates from unemployment ðthe long-term unemployedÞ. The generalized framework is better able to account for long-term unemployment during recessions, whereas Shimer's framework with a homogeneous job finding rate significantly understates it. The extended framework also increases the inflow contribution to unemployment relative to Shimer's study.

A. Current Population Survey ðCPSÞ
We use monthly CPS data between 2002 and 2013 ðending in April 2013Þ, limiting the sample to individuals between the ages of 25 and 55. We focus on this prime-age sample to enable us to ignore issues of delayed labor force entry of younger workers and changes in retirement patterns of older workers. We use these CPS data in several ways. First, we use repeated cross-sectional data when investigating the role of composition, limiting the sample to unemployed workers. Second, we use both cross-sectional and panel data ðmerging individuals across months to build panel dataÞ to investigate the role of duration dependence and nonparticipation. For this exercise, we use data on all employed, unemployed, and nonparticipants. In the cross section, we keep track of the total population of each category to estimate the "stocks." To create panel data, we match observations across successive months, matching on household identifier, line number, age, gender, and race. We use the matched panel data in addition to the CPS cross-sectional estimates of the unemployed, the employed, and nonparticipants to estimate the transition rates between unemployment, employment, and nonparticipation in each month. We also compute overall ðpre-2008Þ transition rates by unemployment duration ðinto both employment and nonparticipationÞ. Finally, we compute transition rates from employment and nonparticipation into unemployment by unemployment duration.

B. Job Openings and Labor Turnover Survey ðJOLTSÞ
We use monthly JOLTS data between 2002 and 2013 to compute the total number of vacancies. We use these vacancy data to calibrate the matching model below during the pre-2008 period. We then use the post-2008 vacancy data as one of the exogenous "forcing variables" for our counterfactual scenarios.

III. Long-Term Unemployment and the Great Recession:
Assessing the Role of Composition Figure 1 shows that the share of the labor force that is long-term unemployed substantially increased during the Great Recession and has remained elevated. We next examine the rise in the share of the currently unemployed with duration exceeding 26 weeks and investigate the role of composition in accounting for this observed increase. Figure 2 ðpanel AÞ illustrates the dramatic increase in long-term unemployment as a share of overall unemployment. The long-term share increased from around 20% at the beginning of 2008 to roughly 45% in 2010. Most of the increase occurred in 2009, a year after the recession began. Moreover, the share remained elevated at around 45% well after the recession officially ended. By comparison, the recession that began in 2001 saw this share increase from roughly 12% to 25%. Similar to the Great Recession, the share increased roughly a year after the recession began and remained elevated for several years after the recession officially ended. Nevertheless, the Great Recession was much deeper than the early 2000s downturn, and it had a substantially larger impact on the structure of unemployment durations.
In this section, we investigate the extent to which the increase in longterm unemployment during the Great Recession can be accounted for by shifting composition in observable characteristics of the unemployed. We do this by investigating the incidence of long-term unemployment over time for several demographic, industry, occupation, geographic, and reasonfor-unemployment groups, along with each group's unemployment share.
Panel A of figure 3 considers the education structure of the unemployed. It shows that the share of long-term unemployment in total unemployment is fairly similar across all education groups. During the recession, long-term unemployment uniformly increased across all education groups. Panel B of figure 3 shows that high school graduates are a larger share of the unemployed than college graduates. During the Great Recession, there is a small increase in the share of college graduates among the unemployed. Despite this, since the rate of long-term unemployment is fairly flat across all education groups, shifts in the education structure of the unemployed cannot account for the changing unemployment duration dynamic during the Great Recession.
Appendix figures C1-C7 ðin appendix C, available onlineÞ consider different observable characteristics. The impact of the Great Recession was widespread, increasing the long-term unemployment share in all major demographic groups, industries, occupations, geographic regions, and reasons for unemployment. The long-term unemployment share also increased in groups by reason for unemployment ðjob losers, those on temporary layoff, job leavers, new entrants, and reentrantsÞ. To quantify how much compositional shifts overall could have explained the rise in long-term unemployment, we hold fixed the long-term unemployment rates for each group in the pre-2008 period and investigate how much observed shifts in group shares can explain the overall rise in long-term unemployment. The aggregated evidence presented in figure 4 shows that compositional changes in the unemployed account for virtually none of the observed rise in long-term unemployment. The rise in long-term unemployment is found for all major labor market groups and is not a demographically isolated phenomenon.

IV. Matching Framework
In this section, we outline our matching framework, which augments a standard matching model to allow for duration dependence in unemployment and flows to and from nonparticipation. We begin with a standard matching model of the labor market ðPissarides 1985; Mortensen and Pissarides 1994Þ, which models fluctuations in the job finding probability through a reduced-form matching function. We enrich this standard matching model to allow for duration dependence in unemployment and we allow a full set of transitions between employment ðEÞ, unemployment ðUÞ, and nonparticipation ðNÞ. 6 Our goal is to calibrate this model using data from before the Great Recession and assess how well it accounts for outflows from unemployment 6 Recent research by Elsby et al. ð2011Þ has highlighted the important role played by nonparticipants in understanding the dynamics of long-term unemployment during the Great Recession.
FIG. 4.-Accounting for long-term unemployment increase from observable compositional shifts. This figure uses data from the Current Population Survey that are summarized in figure 3 and appendix C, figures C1-C7, in order to estimate the role of composition. The predicted long-term unemployment share is calculated by multiplying the pre-2008 average long-term unemployment share by demographic group by the change in the share of unemployed with that characteristic. This procedure is repeated for each observable characteristic ðe.g., education, age, gender, etc.Þ described in figures 3 and C1-C7 to construct the prediction shown in this figure. A color version of this figure is available online. and nonparticipation into employment between 2008 and 2013. Throughout our analysis, we take the number of vacancies and inflows into unemployment and nonparticipation as given. These are the exogenous "forcing variables" of the model. The endogenous variables are the full distribution of unemployment durations, the population shares in each labor market state, and the job finding rates of the unemployed and nonparticipants.
To introduce the model, we begin with the following notation: 1. P t 5 population size ðt is monthly calendar timeÞ and fE t , U t g 5 number of employed and unemployed individuals with associated rates fe t 5 E t =P t ; u t 5 U t =P t g. Note that the unemployment rate is defined relative to the total population ðrather than the labor forceÞ, which imposes symmetry with the nonparticipation rate defined below. 2. N t 5 P t 2 E t 2 U t 5 number of nonparticipants. Let the size of the labor force be denoted by L t 5 E t 1 U t and the nonparticipation rate by n t 5 N t =P t . 3. V t 5 total number of job vacancies. The number of job vacancies is an exogenous forcing variable during the period 2008-13 in the counterfactual scenarios we describe below. 4. Flows to unemployment: l EU t ðemployment → unemploymentÞ, l NU t ðnonparticipation → unemploymentÞ. Both of these transition rates are forcing variables during the period 2008-13. 5. Flows to employment: l UE t ðunemployment → employmentÞ, l NE t ðnonparticipation → employmentÞ. These job finding rates are allowed to endogenously evolve during the period 2008-13. 6. Flows to nonparticipation: l EN t ðemployment → nonparticipationÞ, l UN t ðunemployment → nonparticipationÞ. Both of these transition rates are forcing variables during the period 2008-13.
Appendix B provides more detail on how each of these transition rates are computed.

A. Labor Market Flows during the Great Recession
We begin by presenting descriptive evidence on labor market flows over time. Figure 5 plots the monthly transition rates to and from employment, unemployment, and nonparticipation. The measured transition rates are adjusted to be consistent with observed changes in stocks between months; appendix B provides the details of this procedure. We also account for seasonality by residualizing out month fixed effects, and we smooth the series by taking 3-month moving averages.
First, we see in panel A of figure 5 that the monthly transition rates from unemployment to employment and nonparticipation dropped sig-nificantly during 2008. Starting in 2010, the flows from unemployment into nonparticipation began to recover and by the end of 2013 were close to their pre-recession levels. On the other hand, the job finding rates of the unemployed ðflows from unemployment to employmentÞ have remained low following the Great Recession.
Second, panel B shows that flows from employment to nonparticipation remained relatively flat during the Great Recession. Job losses leading to unemployment ðemployment to unemployment flowsÞ spiked up in the Great Recession in 2008-9 and have slowly come back down in the recovery.
Third, panel C shows that job finding rates of nonparticipants ðflows from nonparticipation to employmentÞ dropped in 2008 and remained low through the end of 2013. While the job finding rate for the unemployed declined sharply and bottomed out in 2009, the job finding rate for nonparticipants fell more smoothly and bottomed out in 2010. On the other hand, flows from nonparticipation to unemployment increased substantially in 2008 and remained high until the end of 2013. Interestingly, in the pre-Great Recession period, the outflow rate from nonparticipation to employment always exceeded the outflow rate to unemployment; however, during the Great Recession, and at least through 2013, the opposite was true. We show below that accounting for flows from nonparticipation to unemployment during the Great Recession is important for understanding the dynamics of the unemployment rate. In particular, we find that ignoring changes in the N-to-U and U-to-N transition rates after 2008 results in a much smaller outward shift in the Beveridge curve according to our calibrated model. 7 Flows from unemployment to employment are in part affected by flows from unemployment to nonparticipation. For example, if more of the unemployed individuals were to withdraw from the labor force, these individuals do not go from unemployment to employment at the same rate. To explore this issue, we define labor market flows for "indomitable job seekers" ðClark and Summers 1979Þ to be the ratio of U-to-E flows to the sum of U-to-E and U-to-U flows. This conceptually corresponds to a hypothetical unemployed job seeker who is unable to exit the labor force ðand thus can only either transition to employment or remain unemployed, perhaps indefinitelyÞ. This "rescaled" U-to-E transition rate is ðmechanicallyÞ higher for indomitable job seekers, as illustrated in panel D of figure 5; however, we also see a similarly sharp drop in the job finding rate for this group during the Great Recession.  We adapt the standard matching function to allow nonparticipants to find jobs. We assume that nonparticipants and unemployed individuals meet job openings according to the function MðU 1 sN; VÞ 5 m 0 ðU 1 sNÞ a V 12a . 8 One may interpret s as the share of the nonparticipants who are "marginally attached," or, alternatively, as the search efficiency of nonparticipants relative to the unemployed, following Jones and Riddell ð1999, 2006Þ. According to Jones and Riddell's estimates, sN is about 25%-30% of the unemployed population, and these ressearchers also find that l UE t is roughly twice as large as l NE t . We assume that the share of meetings with unemployed individuals is given by U/ðU 1 sNÞ, while the remaining share is with nonparticipants. In addition, we assume ðfor the unemployedÞ that the probability that a meeting results in a hire depends on the duration of unemployment. In particular, Aðd Þ gives the relative hiring probability of an individual with unemployment duration d as compared to a newly unemployed individual ðwith duration d 5 0Þ. These assumptions imply that the job finding rates for the unemployed and nonparticipants are given, respectively, by the following expressions: where x t 5 V t =ðU t 1 sN t Þ is a measure of labor market tightness and d is the duration of unemployment. The parametric specification for l UE t ðdÞ assumes that there is "true" duration dependence in job finding rates out of unemployment, that is, a genuine causal effect of longer unemployment durations on the hazard rate of exit out of unemployment ðHeckman and Singer 1984Þ.
We propose a parametric specification for AðdÞ and estimate this function in the pre-Great Recession period, as we describe below. Let the probability density and distribution of ongoing unemployment durations be given by v t ðdÞ and V t , respectively. By integrating over the duration distribution, we get the average job finding rate for the unemployed: l UE How does a recession affect the unemployment job finding rate? In a recession, x t falls, lowering l UE t ðx t ; tÞ, and hence l UE t ðx t Þ. The fall in l UE t ðx t Þ affects v t ðtÞ, which can feed back into a lower l UE t ðx t Þ through duration dependence and consequently a higher unemployment rate.
Note that where A t 5 ∫ AðtÞv t ðtÞdt. With empirical estimates for A t and the job finding rates, we can solve for s 5A t ðl NE t =l UE t Þ. The right-hand side varies with t, but we assume that s is time invariant, so we can simply take the average of this expression in period 2002-7 to produce an estimate of s to use in our calibrations. Note that we also assume that both m 0 and AðdÞ are time invariant: there are no cyclical changes in matching efficiency or cyclical variation in the magnitude of duration dependence. We explore alternative assumptions on how AðdÞ varies over the business cycle in sensitivity analysis below, while cyclical variation in the matching efficiency parameter is studied in detail in Sahin et al. ð2014Þ.

C. Labor Market Dynamics
Given the transition rates between employment, unemployment, and nonparticipation, we can express the dynamics of each of these populations as follows: In these dynamic equations, we have placed hats abovel NE t andl UE t ðdÞ to emphasize that these rates are endogenous in our counterfactual simulations. When we construct the counterfactual scenarios, we assume that if nonparticipants move to unemployment, they draw an unemployment duration from the ðempiricalÞ distribution of unemployment durations estimated from observed N-to-U transitions ðwhere the empirical distribution is reestimated each quarter for three unemployment categories: ½0-6Þ months, ½6-12Þ months, and ≥ 12 monthsÞ. Similarly, we also account for the fact that a share of entrants into unemployment from employment report unemployment durations of 6 months or longer, so when employed workers move into unemployment, they draw an unemployment duration from the empirical distribution of unemployment durations ðestimated analogously as for nonparticipants aboveÞ. These two empirical distributions are v NU t ðdÞ and v EU t ðdÞ, respectively. Since this share changes over time and increased during the Great Recession, we estimate these distributions in each year-quarter, and we use this time-varying distribution in our counterfactual simulations.
In the next section, we examine the incidence of long-term unemployment and the Beveridge curve. The share of unemployed individuals at calendar time t who have been out of work longer than t weeks is given by where U t ðdÞ is defined by equations ð3Þ and ð4Þ. We use this as our measure of the share of unemployed individuals who are long-term unemployed, and we focus on t 5 26 weeks and t 5 52 weeks. When we plot the Beveridge curve, we plot the the total unemployed individuals as predicted by our model against the total observed number of job vacancies, normalizing both measures by the total population ði.e., U t /ðE t 1 U t 1 N t Þ and V t /ðE t 1 U t 1 N t ÞÞ. Since our matching model focuses on capturing job finding rates of both unemployed and nonparticipants, we include the total population rather than the total labor force in the denominator.

D. Counterfactual Scenarios
The goal of our calibrations is to assess how far our enriched matching model can go in accounting for the rise in long-term unemployment and the outward shift in the Beveridge curve during the Great Recession. We also investigate the relationship between the nonparticipation rate and the vacancy rate. Our approach is to estimate the model fundamentals during the period 2002-7 on monthly CPS ðpanel and pooled cross-sectionalÞ data and then assess the model by comparing our counterfactual predictions to observed labor market outcomes during the period 2008-13. We estimate duration dependence in the job finding rate from unemployment ðhow l UE t varies with durationÞ, the search effectiveness of the marginally attached ðsÞ, and the overall matching efficiency m 0 and matching technology parameter a. Our model uses as exogenous forcing variables shifts in labor demand-where labor demand is proxied for by V t ; l EU t ; À l EN t Þ-and shifts between unemployment and nonparticipation versus unemployment, l UN t ; l NU t À Á . Thus, we fix the pattern of duration dependence, as reflected in AðdÞ, and we allow the job finding rates l UE t ðdÞ and l NE t -and consequently the entire distribution of unemployment durations-to evolve endogenously during the Great Recession. Our methodology follows Shimer ð2005Þ by treating the separation rates of em-ployed workers from their jobs, l EU t and l EN t , as exogenous. Shimer also considers exogenous productivity shocks in his model, which affects the equilibrium level of vacancies. We do not explicitly model the determination of vacancies; rather, we take a more reduced-form approach and instead treat vacancies as exogenous. Finally, we view flows between nonparticipation and unemployment as being "outside the model" since they may reflect factors such as the extension of UI benefits.
In terms of predicting the incidence of long-term unemployment, we rely on the cross-sectional share of workers with ongoing unemployment spells exceeding 26 and 52 weeks, respectively. For predicting stocks of unemployment, employment, and nonparticipation over time, we use the dynamic equations above to simulate the model.

V. Calibration Methodology
We calibrate the model in the following steps.
Appendix B describes how we estimate the transition rates l ij t from the monthly CPS cross-sections and the ðmatchedÞ panel data component of the CPS.
2. An important issue is how we allocate flows from nonparticipation to unemployment of various durations. Elsby et al. ð2011Þ show that roughly 60% of the inflows into unemployment at reported durations longer than 1 month originate from nonparticipation. It appears that there are marginally attached workers who alternate between unemployment and nonparticipation, and when these workers return to unemployment, they often report a duration that may include time since they separated from their last employer as opposed to duration of unemployment spell since last leaving nonparticipation. Panel A of figure 6 sheds light on this issue by plotting the share of flows from nonparticipation to unemployment of a particular duration. We see that in the pre-recession period, roughly half of the flows had durations less than or equal to 1 month; however, during the Great Recession, this share dropped substantially to around 30%. On the other hand, the share of flows with durations longer than 12 months increased from roughly 20% to over 30%. In light of this, we collapse the 2002-13 data quarterly, and each quarter we estimate the empirical distribution of unemployment durations that nonparticipants transition into. Therefore, for our post-2008 counterfactuals, we use this empirical distribution for each N-to-U transition implied by the dynamic equations of the model and the observed unemployment durations that the nonparticipants are transitioning into.
3. Another important issue is how we allocate flows from employment to unemployment of various durations. Panel B of figure 6 plots the share of E-to-U flows going to a given unemployment duration. In interpret-ing the shares in this figure, note that the scale of the left ðrightÞ axis is for durations less than or equal to ðgreater thanÞ 1 month. We see that in the pre-recession period, roughly 80%-85% of the transitions from employment to unemployment report durations less than or equal to 1 month. However, this share falls to 70% during the Great Recession. We follow an analogous procedure as in the previous step, estimating the empirical distribution of unemployment durations that employed workers transition into ðfor each quarterÞ, and we use this distribution in our counterfactual scenarios for each E-to-U transition. 4. We use the measured relative job finding rates at different durations ðl UE t ðdÞÞ to estimate AðdÞ. For the period 2002-7, we fit a curve through the empirical estimates of l UE t ðdÞ, normalized by l UE t ð0Þ, using the following functional form AðdÞ 5 ð1 2 a 1 2 a 2 Þ 1 a 1 exp ð2b 1 Â dÞ 1 a 2 exp ð2b 2 Â dÞ. See panel A of figure 7 for our preferred estimate ofÂðd Þ. The estimates FIG. 6.-"Incoming" unemployment duration distributions. These figures report the share of individuals transitioning into unemployment from either nonparticipation ðpanel AÞ or employment ðpanel BÞ. The figures show the share of workers transitioning into unemployment by unemployment duration. This reveals the extent to which unemployed individuals who did not report being unemployed in the previous month report unemployment durations that are inconsistent with being a newly unemployed worker. We report annual averages in this figure but use quarterly averages in the counterfactual simulations ðand group ½0, 6Þ months to-getherÞ. A color version of this figure is available online. reported in table 1 areâ 1 5 0:314;â 2 5 0:393,b 1 5 1:085, andb 2 5 0:055. We find that the job finding rate declines sharply for the first 8-10 months of unemployment and then declines much less steeply after that. The declining job finding rate with duration of unemployment can reflect "true" negative duration dependence in which the longer any individual is unemployed, the lower becomes the job finding rate. Alternatively, it could reflect heterogeneity among the unemployed, with the remaining pool of the unemployed being more negatively selected at longer durations. To investigate this, we reestimate AðdÞ, controlling for a very rich set of observable characteristics available in the CPS: gender, fifth-degree polynomial in age, three race categories ðwhite, black, otherÞ, five education groups ðhigh school dropout, high school graduate, some college, college graduate, advanced degreeÞ, and gender interactions for all of the age, race, and education variables. When we control for these observable characteristics, we continue to find that the job finding rate ðconditional on observ-ablesÞ declines sharply with unemployment duration; moreover, the estimated decline is very similar to the results from estimating AðdÞ without controls, as can be seen by comparing the solid line ðwith controlsÞ to the dashed line ðwithout controlsÞ in panel A of figure 7.
Of course, these results do not rule out the existence of unobserved heterogeneity-such as differences in recall rates to one's previous job as -Duration dependence and predicted unemployment job finding probability. In panel A, the figure uses data from the Current Population Survey and estimates ðvia nonlinear least squaresÞ the negative exponential relationship between monthly job finding probability and unemployment duration. The NLLS uses CPS sample weights. The following functional form is used to estimate duration dependence: AðdÞ 5 ð1 2 a 1 2 a 2 Þ 1 a 1 exp ð2b 1 Â d Þ 1 a 2 expð2b 2 Â dÞ. The fitted values from the estimates with controls ðsolid lineÞ are used to construct the counterfactuals shown in figures 7-10. The controls used are the following: gender, fifth-degree polynomial in age, three race dummies ðwhite, black, otherÞ, five education category dummies ðhigh school dropout, high school graduate, some college, college graduate, and otherÞ, and gender interactions for all of the age, race, and education variables. Only monthly cell means with at least 30 observations are shown. In panel B, the figure is generated by using estimates of how job finding probability varies with unemployment duration interacted with observed distribution of unemployment durations. Thus, the line in this figure shows the extent to which we would predict changes in job finding probability based solely on observed changes in distribution of unemployment duration. The y-axis scale is normalized so that a value of 1 indicates average job finding probability for a newly unemployed worker. A color version of this figure is available online. be consistent with recent resume audit studies finding that job applications with longer employment gaps ðlonger duration of unemploymentÞ get lower callback rates than those with implied shorter unemployment duration ðGhayad 2013; Kroft et al. 2013; Eriksson and Rooth 2014Þ. We  note that the pattern of negative duration dependence after controlling for the observables in the CPS in panel A of figure 7 is fairly similar to the results of declining employer callback rates with unemployment duration in the audit study of Kroft et al. ð2013Þ, which we also use in alternative counterfactual scenarios below. In our main results, we use the estimates of Aðd Þ, which includes the large set of controls described above. The results of the alternative duration dependence estimates are reported in table 2. Given the concerns about Aðd Þ not representing the causal effect of longer unemployment durations, we also make adjustments to AðdÞ assuming that, say, 50% of the observed duration dependence reflects a genuine causal effect.
5. Next, we estimate the parameters of the matching function by minimizing the distance between the observed job finding rates and the job finding rates implied by the matching functions using monthly CPS and JOLTS data for the period 2002-7. The implied job finding rates for a given parameter vector ðs, m 0 , aÞ, taking estimated parameters of AðdÞ as given are the following:  5 ð1 2 a 1 2 a 2 Þ 1 a 1 expð2b 1 Â dÞ 1 a 2 expð2b The minimum distance estimates are reported in table 1 and are as follows:â 5 0:753,m 0 5 0:435, andŝ 5 0:218. 6. Finally, we use V t ; l EU t ; l EN t ; l UN t ; l NU t È É t ≥1=2008 as the exogenous forcing variables to form our counterfactual predictions below.

A. Predicted Job Finding Rates
During the Great Recession, average job finding rates declined in part because average unemployment durations increased. Panel B in figure 7 shows what happened to average job finding rates due to the increase in durations by plotting A t 5 ∫ AðtÞv t ðtÞdt from 2002 to 2013. Here A t is a useful measure of the duration structure of unemployment since it summarizes how the duration structure affects the average job finding rate assuming that Aðd Þ describes the effect of unemployment duration on the job finding rate. We use the estimated AðdÞ, which controls for the rich set of observable characteristics available in the CPS ðgender, age, race, and educationÞ. To the extent that the recession shifted the unemployed toward longer durations, this will lower A t since A 0 ðtÞ < 0. 9 We see that, starting in 2008, there was a sharp drop in A t from around 0.75 to roughly 0.63 ðwhere Að0Þ is normalized to 1, so that AðdÞ can be interpreted as the relative job finding rate for high durations compared to the newly unemployedÞ. This figure therefore shows that the indirect effect of a drop in market tightness on the average job finding rate is quantitatively important, and it suggests the possibility of a prominent role for negative duration dependence in the job finding rate out of unemployment in accounting for changes in long-term unemployment share as well as an outward shift in the Beveridge curve.
In panels A and B of figure 8, we plot the predicted and observed job finding rates for the unemployed and nonparticipants, respectively. 10 These transition rates are the two key endogenous variables of the model. By construction, the predicted rates match the observed rates in the pre-Great- Recession period. During the Great Recession, we see that the model does a reasonable job of predicting the job finding rate for the unemployed; however, nonparticipants were not filling jobs at the rate they were predicted to during this time period. This suggests that there was something fundamentally different about the Great Recession in terms of its impact on individuals out of the labor force that is at odds with the behavior of this group in the pre-recession period. We investigate this issue below.

B. Long-Term Unemployment
Panel A in figure 9 investigates how well our calibrated model matches the observed increase in incidence of long-term unemployment. The calibrated model fits the data by construction up to the final quarter of 2007. From 2008 onward, we use the job finding rates for the unemployed and nonparticipants that are predicted by our model. We label the data generated by model as "Counterfactual." Panel A of figure 9 shows that our model does very well in accounting for the observed increase in share of unemployed that are long-term unemployed when long-term unemployment is defined to be > 26 weeks. In panel B of figure 9, long-term unemployment is now defined to be > 52 weeks. In this case, our model does not do quite as well, although it still accounts for a large share of the actual increase in long-term unemployment. The relatively poorer fit for long-term unemployment > 52 weeks could be partly due to the fact that the estimated AðdÞ-which controls how job finding probability falls with unemployment duration-declines sharply during the first several months and declines much less steeply after that.

C. Beveridge Curve
Panel C of figure 9 plots the Beveridge curve using unemployment and vacancy rates, where the denominator in each case is defined as total population between ages 25 and 55. We plot two curves in this figure. The solid curve, labeled "Observed," plots the actual unemployment and vacancy rate in a given quarter. Next, the dotted curve, labeled "Counterfactual," plots the predicted unemployment along with the observed vacancy rate for the quarters starting with 2008Q1. The figure shows a significant spike in unemployment during the first quarter of 2008. At this point, vacancies were very low compared to the 2002-7 period. However, even as vacancy rates recovered during 2010 and 2011, the number of unemployed declined only very slowly. It seems as if the Beveridge curve has shifted out. This is a manifestation of what has been dubbed the "jobless recovery." Overall, we see that our model also predicts an outward shift in the Beveridge curve during the Great Recession, although by not as much as observed. This is because, while our model accounts  for the rise in the long-term unemployed share of total unemployment, it somewhat underpredicts the overall unemployment rate.

D. Nonparticipation and Vacancies
We next investigate the relationship between nonparticipation and vacancy rates. Panel D of figure 9 is identical to panel C of figure 9, except that we consider rates of nonparticipation instead of unemployment rates ðwhere again the total population P 5 L 1 N 5 E 1 U 1 N is the de-nominatorÞ. Although our model does a reasonably good job of describing the relationship between unemployment and vacancies, it does a very poor job of fitting the relationship between nonparticipation rates and vacancies. In particular, the model substantially underpredicts nonparticipation rates during the Great Recession. This is primarily due to the fact that the predicted job finding rate for nonparticipants is too high.

E. Alternative Assumptions Regarding Duration Dependence
Our last sensitivity analysis examines whether our results are sensitive to using alternative estimates of duration dependence. These results are reported in figure 10, where we compare the predicted increase in longterm unemployment, defined as the share of the unemployed with ongoing durations exceeding 26 week, under several scenarios. In panel A, we report results that estimate AðdÞ from the CPS controlling for a rich set of observables, as well as results that impose the AðdÞ function that most closely matches the experimental estimates in Kroft et al. ð2013Þ. One of the scenarios uses the experimental estimates from the overall sample, while another scenario allows AðdÞ to vary with the unemployment rate. In our baseline calibration, we assume that Aðd Þ is stable over the business cycle, while Kroft et al. ð2013Þ present evidence that suggests that the magnitude of duration dependence is smaller when the unemployment rate is relatively high. We therefore allow Aðd Þ to vary with the unemployment based on experimental estimates and calibrate the model with this alternative assumption on duration dependence. Overall, we find that the predictions are fairly similar across these scenarios, reflecting the fact that the estimate of duration dependence in the CPS ðwith and without controlsÞ is fairly similar to the experimental estimates in Kroft et al. ð2013Þ.
Next, in panel B of figure 10, we re-scale the CPS estimate of AðdÞ by assuming that only a fixed percentage represents "true" duration dependence ði.e., a genuine causal effect of unemployment duration on job finding rateÞ. When we assume that only 50% of observed duration dependence is causal, we still find that our calibrated model can account for a large share of the rise in long-term unemployment. This is because even in this scenario the job finding rate still falls sharply over the first 6 months of unemployment.

A. Ignoring Duration Dependence
We next demonstrate that accounting for duration dependence in job finding rates is crucial for this success in matching the data. To do this, we reestimate the matching model setting AðdÞ 5 1. The results of this exercise are reported in figure 11, where panels A and B report long-term unemployment shares and panels C and D report the Beveridge curve and the curve relating nonparticipation rates to vacancy rates, respectively. Panels A and B show that the predicted long-term unemployment from model calibration ignoring duration dependence is much lower than the predicted long-term unemployment we get when accounting for negative duration dependence in the exit rate from unemployment. Thus, duration dependence in job finding rates is empirically important in understanding the historical increase in long-term unemployment during the Great Recession.
Turning to the Beveridge curve in panel C, we see that the model does worse when ignoring duration dependence in terms of predicting the observed unemployment rate during the Great Recession. This is clear visual evidence that a standard matching model-without negative duration dependence-underpredicts unemployment. On the other hand, panel D shows that the magnitude of duration dependence does not substantially affect predicted nonparticipation rates, although duration dependence does appear to begin to matter for calibrations during the last few quarters of the sample period. 11 B. Counterfactual Scenarios Ignoring Nonparticipation Figure 12 considers a counterfactual that holds all flows to and from nonparticipation constant at their 2007 values ðexcept for the N-to-E flow, which is determined endogenously by the matching functionÞ. It is evident from panels A-C that ignoring the nonparticipation margin leads one to substantially underpredict overall unemployment and the structure of unemployment during the Great Recession. We also see in panel D that rather than underpredicting nonparticipation rates as in the baseline calibration, we now substantially overpredict these rates. Intuitively, by ignoring the increase in N-to-U flows and the decrease in U-to-N flows that occurred during the Great Recession, we instead predict nonparticipation rates that are much too high. Therefore, accounting for nonparticipation flows is crucial in understanding the dynamics of unemployment during the Great Recession. This is related to ðand consistent withÞ the findings in Elsby et al. ð2015Þ, which reports that the participation margin accounts for one-third of the cyclical variation in the unemployment rate. We next consider ignoring flows to and from nonparticipation one by one. The short dashed line allows AðdÞ to vary with labor market conditions, as found in Kroft et al. ð2013Þ; specifically, AðdÞ is flatter than average when the unemployment rate exceeds 8.8% ðin April 2009Þ and steeper before that point. In panel B, the figure shows robustness to assuming that the estimated AðdÞ function recovers a mixture of "true" duration dependence and unobserved heterogeneity. By making assumptions on the share of unobserved heterogeneity captured by the function, AðdÞ can be rescaled to be a measure of "true" duration dependence. A color version of this figure is available online.

Ignoring Changes in N-to-U
We saw in figure 5 that transitions from nonparticipation to unemployment rose significantly during the Great Recession. Moreover, we know from research by Elsby et al. ð2011Þ that some of the transitions from nonparticipation to unemployment go to long durations. We next examine the importance of these flows by holding N-to-U rates fixed at their values in December 2007. Panels A and B of figure C8 show that the predicted longterm shares fall somewhat relative to the counterfactual that does not fix these flows. Additionally, when the N-to-U flows are fixed at their 2007 values, the model is less able to match the outward shift in the Beveridge curve. Overall, these transitions appear to be somewhat important to understanding the rise in long-term and overall unemployment during the Great Recession. 12 Interestingly, the evidence in panel D suggests the alternative model is better able to explain the dynamics of nonparticipation. 12 It is worth emphasizing, however, that if one were to form the counterfactuals by assuming that all transitions from nonparticipation to unemployment go to 0 months of duration, the prediction would be very poor.

Ignoring Changes in U-to-N
Another fact about the Great Recession is that flows from unemployment to nonparticipation significantly declined, at least from 2008 to 2010. Elsby et al. ð2015Þ document the procyclicality of these flows during recessions since 1970. They argue that in recessions, the composition of the unemployed shifts to those who are more "attached" to the labor market and that this explains three-quarters of the drop in the flow rate from unemployment to nonparticipation. 13 We examine the importance of this change during the Great Recession by holding U-to-N rates fixed at their values in December 2007. The results are reported in figure C9 and show that the model somewhat underpredicts long-term unemployment and also the overall level of unemployment, at least until the end of 2010. Why are these flows so important for understanding long-term unemployment and the movement of the Beveridge curve? Intuitively, if we assumed more transitions from unemployment to nonparticipation than was actually the case, this would lower the stock of the unemployed and lead to a lower unemployment rate.

Ignoring Changes in E-to-N
Finally, figure C10 investigates the flows from E-to-N, which were largely stable during the Great Recession, according to the results in figure 5. Therefore, it is not surprising to see that the model predictions do not substantively change when we "shut down" changes in E-to-N flows by holding them at their December 2007 values.

C. Comparison to the 1981 Recession
The 1981-82 recession generated double-digit unemployment similar to peak unemployment in the Great Recession, but long-term unemployment did not rise nearly as much in the early 1980s' downturn. It is useful to consider what would have happened to long-term unemployment if vacancies had evolved as in the early 1980s recession as opposed to the way they evolved during the Great Recession. 14 Panel A of figure 13 shows the ðrelativeÞ differences in evolution of vacancies between the two recessions. The vacancy data for the 1981 recession are filtered data from Help Wanted Index from Elsby et al. ð2011Þ. Compared to vacancies during the Great Recession, in the early 1980s vacancies fell by roughly the same order of magnitude but rebounded much more quickly. Panel B in figure 13 displays the model predictions for long-term unemployment using vacancies in the 1981 recession as the forcing variable in the model ðin place of the 2008 recessionÞ. We see that the predicted long-term unemployment share is much lower than the share predicted during the Great Recession. Thus, our model is able to provide an explanation for why long-term unemployment rose much more sharply in the Great Recession as compared to the 1981 recession, arising from a more sustained decline and much weaker recovery in labor demand ðas reflected in the vacancy rateÞ.

D. The Beveridge Curve and Long-Term Unemployment
Ghayad and Dickens ð2012Þ consider the recent outward shift in the Beveridge curve and note that it occurred over a period of less than 1 year as compared to the roughly 8 years it took for the Beveridge curve to shift in the recession of the 1970s. They also note that if one constructs separate Beveridge curves for the short-term and long-term unemployed, all of the movement in the aggregate Beveridge curve is relative to the longterm unemployment rate. This is mechanically related to the durationspecific unemployment rates discussed in figure 1 above.
Our results can help account for these findings. First, we saw that long-term unemployment increased rapidly over a short period of time. This change, combined with negative duration dependence in job finding rates, helps explain the fast shift in the Beveridge curve. To shed light on the second finding, in figure C11, we plot two separate Beveridge curves, one for the short-term unemployed ðpanel AÞ and one for the long-term unemployed ðpanel BÞ. Similar to Ghayad and Dickens ð2012Þ, we see that the shift in the overall Beveridge curve is due to the shift in the Beveridge curve for the long-term unemployed. We also see that our model is unable to completely account for these shifts in both curves. In particular, it tends to predict too large a drop in unemployment for the later years of the Great Recession for both curves. The next subsection provides some explanations for the difficulty of the model to fully explain some of the stylized facts of the Great Recession.

E. Alternative Explanations
Our results indicate that our model can account for unemployment dynamics reasonably well but has a harder time matching dynamics among nonparticipants. One possibility is that those who drop out of the labor force during the Great Recession may be less marginally attached ðless likely to be interested in workÞ than those who drop out during normal times. In other words, it might be the case that s falls during the Great Recession in a way that we are not accounting for in the matching framework and this could explain some of the discrepancy.
We examine this possibility in panel A of figure 14, which plots the share of nonparticipants who are "discouraged" and the share of nonparticipants FIG. 14.-Changing composition of labor force nonparticipants. These figures report statistics from the Current Population Survey on the share of nonparticipants who report either being "discouraged" or saying that they "want a job." In panel B, the monthly job finding rates for unemployed, nonparticipants ðoverallÞ, and nonparticipants ðwho are in "want a job" categoryÞ are displayed between 2002 and 2013. A color version of this figure is available online. who report that they want a job. The figure shows that, starting in 2008, both increased sharply. This suggests that s actually increased during the Great Recession and that if we were to account for this change in our matching framework, then our model-based predictions would likely be even worse. Panel B of figure 14 plots the transition rates from nonparticipation to employment-for those who report that they want to work. We see that for this group, the job finding rate fell during the Great Recession. We are thus left with an incomplete understanding of why nonparticipants did not find jobs at the rate predicted by our calibrated model.
We conclude with several speculative thoughts regarding other possible explanations of the lower-than-expected job finding rate of nonparticipants. First, our model does not capture the possibility of negative duration dependence in job finding rates for nonparticipants; the model only allows for duration dependence in unemployment. Recent work by Autor et al. ð2015Þ reports strong evidence that additional months out of the labor force has a negative causal effect on probability of employment. 15 Unfortunately, we cannot readily estimate such duration dependence in the job finding rate of labor market nonparticipants since the CPS does not record time spent out of the labor force. Second, our model ignores factors such as the recent rise in Social Security Disability Insurance ðSSDIÞ applications and SSDI enrollments in the Great Recession. Third, the dynamics of our calibrated matching model may possibly obscure other changing features of the labor market during times of weak aggregate demand. For example, models of "queuing" and "ranking" may feature discouraged and/or marginally attached workers ending up at the end of the queue, and this could lead to long-term joblessness ðOkun 1973; Blanchard and Diamond 1994Þ. Finally, some adult workers may be returning to school and/ or job training and not looking for work ðBarr and Turner 2013Þ. This would represent a compositional change that would reduce the job finding rate for nonparticipants in a way that could potentially account for the residual decline not accounted for by our calibrated model.

VIII. Conclusion
Both short-term and long-term unemployment increased sharply in 2008-9 during the Great Recession. But while short-term unemployment returned to normal levels by 2013, long-term unemployment remains at historically high levels in the aftermath of the Great Recession. We showed that long-term unemployment increased for virtually all groups and that shifts in observable characteristics of the unemployed do not go very far in accounting for the rise in long-term unemployment.
By contrast, an enriched matching model that allows for duration dependence in unemployment and transitions between employment ðEÞ, unemployment ðUÞ, and nonparticipation ðNÞ can account for almost all of the increase in the incidence of long-term unemployment and much of the observed outward shift in the Beveridge curve between 2008 and 2013. We emphasize that duration dependence is not the primary force behind rising long-term unemployment in the Great Recession per se; rather, duration dependence serves to reinforce and amplify the initial labor demand shock that shifted the distribution of unemployment durations. Our results suggest that both negative duration dependence in the job finding rate out of unemployment and transitions to ðand fromÞ nonparticipation may play an important part in understanding both the rise in long-term unemployment and the observed outward shift in the Beveridge curve.
Much evidence suggests that there is sizable causal negative duration dependence in the escape rate from unemployment. The longer one has been unemployed, the less likely one is to get a callback from an employer, and job search effort also is likely to decline. A strong negative labor demand shock like from a major financial crisis and/or from consumer, firm, and lender behavior can build up the stock of the long-term unemployed. Negative duration dependence means that the long-term unemployed are less effective job seekers than the short-term unemployed. Thus, the rise in long-term unemployment itself can help explain much of the outward shift in the traditional Beveridge curve following the Great Recession. Essentially, the overall matching efficiency of the labor market is reduced when the incidence of long-term unemployment is high. This is not the whole story, however. Firms continue to worry about demand conditions and have lowered their recruiting intensity for posted vacancies ðDavis et al. 2013Þ, further contributing to the outward Beveridge curve shift and the persistence of the low flows from unemployment to employment in the aftermath of the Great Recession.

Appendix A Data Sources
These are the data sources used for both calibration ðwhich only uses pre-1/2008 dataÞ and counterfactual estimation ðwhich uses post-1/2008 dataÞ: • V t ðduration distributionÞ: CPS monthly data from the period 1/ 2002-1/2013. We estimate the unemployment duration distribution monthly for all unemployed adults aged 25-55. We group all unem-ployment durations greater than or equal to 24 months together in a single category, and the rest of the durations are grouped by month. • V t ðvacanciesÞ: JOLTS monthly data between 1/2002 and 1/2013. We use the seasonally unadjusted data released by the BLS and residualize out month fixed effects to account for seasonality and then calculate three-month moving averages to smooth the series. • U t , E t , N t ðstocks of unemployed, employed, and nonparticipantsÞ: CPS monthly data between 1/2002 and 1/2013. We use CPS survey weights to estimate stocks in each month for each group for our baseline sample of adults aged 25-55. • l UE t ; l UN t ; l EU t ; l EN t ; l NE t ; l NU t È É ðtransition rates between E/U/NÞ: CPS monthly data between 1/2002 and 1/2013. See appendix B for more details on construction of these panel transition rates, which are based on matching individuals across months as in Shimer ð2012Þ.
• AðdÞ ðduration dependence functionÞ: We estimate AðdÞ in several ways. For the main results, we use job finding rate for unemployed workers ðby unemployment duration in monthsÞ pooling all monthly CPS data between 1/2002 and 12/2007. The job finding rate is defined as the monthly probability that a given unemployed job seeker reports employment in both of the following 2 months ðthe requirement of 2 months follows Rothstein 2011; see references therein for discussion and justificationÞ. For robustness, we also use estimates of AðdÞ from the experimental data in Kroft et al. ð2013Þ; see the main text for more details.
Using the data sources above, we calibrate a, m 0 , s ðmatching function parametersÞ using data from before 1/2008. See the main text for more details. This leaves us with the following system of equations: 8. We recover Aðd Þ from the panel data job finding rates for the unemployed.