Job Duration Over the Business Cycle. José Mustre-del-Río November 2012; Updated June 2017 RWP 12-08

Transcription

1 Job Duration Over the Business Cycle José Mustre-del-Río November 2012; Updated June 2017 RWP 12-08

2 Job Duration Over the Business Cycle José Mustre-del-Río Federal Reserve Bank of Kansas City June 2017 Abstract Evidence from the National Longitudinal Survey of Youth (NLSY) suggests the cyclicality of job duration depends on the worker s prior and future employment status. For example, duration is pro-cyclical for matches where the worker was previously nonemployed and will become nonemployed once the match ends. However, duration is countercyclical for matches where the worker was previously nonemployed and transitions to another job following the dissolution of the match. Importantly, these results are not entirely captured by differences in starting wages. Keywords: Job duration, business cycles, search and matching, wages. JEL classification: E24, E32, J21, J22, J62, J63, J64. This paper has greatly benefited from the comments of two anonymous referees. The author also thanks Mark Bils, Yongsung Chang, Mary Daly, Jessica Ford, William Hawkins, Toshihiko Mukoyama, Nick Sly, Willem Van Zandweghe, Benjamín Villena-Roldán, and seminar participants at Rochester and the Kansas City Fed for useful discussions and comments. Excellent research assistance was provided by William Xu. The views expressed in this paper are solely those of the author and do not necessarily represent the views of the Federal Reserve Bank of Kansas City or the Federal Reserve System. jose.mustre-del-rio@kc.frb.org.

3 Knowing how long a worker-firm match is expected to last and whether this duration varies with the business cycle is crucial for understanding many decisions in the labor market. For example, if matches formed in booms are expected to be long-lived (e.g. because aggregate productivity is expected to be persistently high), then any positive surplus is expected to accrue to each party over a long time horizon, thus providing impetus for workers to search in the market and firms to post vacancies. However, if matches formed in expansions are expected to be short-lived (e.g. because they are stepping stones for workers in between jobs), then firms may either post fewer vacancies or adjust starting pay to entice workers to stay in the match. This paper presents new evidence on how match duration varies over the cycle, whether it depends on the worker s employment history, and whether it is internalized by starting wages. Data from the National Longitudinal Survey of Youth (NLSY) suggests the cyclicality of duration does depend on the worker s prior and future employment status. Additionally, the results suggests differences in starting wages do not fully account for differences in expected duration over the cycle. More precisely, the data suggests the following. First, duration is pro-cyclical and not internalized by starting wages for NE to NE matches; i.e. those formed by a previously nonemployed worker who will become nonemployed once the match ends. For these matches, expected duration rises if they begin in booms, and falls as current conditions deteriorate. From a modeling standpoint, this finding is consistent with these matches having low surplus in expansions, which turns negative in recessions. Consistently, the data shows workers in these matches are less educated than average. Second, duration is counter-cyclical and not internalized by starting wages for NE to E matches; i.e. those formed by a previously nonemployed worker who transitions to another job once the current one ends. For these matches, expected duration falls if the begin in expansions, but rises as current conditions deteriorate. This finding highlights how on-the-job search affects duration. At the start of the match the labor market is tight and the job-to-job 2

4 transition rate is high, which raises the likelihood of the matching ending. However, as the labor market becomes slack, the job-to-job transition rate falls and so does the likelihood of the match ending in the immediate future. Third, duration is pro-cyclical, but internalized by starting wages for E to E matches; i.e. those formed by a worker who just executed a job-to-job transition and who will execute another one once the match ends. These observations are also consistent with a model of on-the-job search as these matches are stepping stone jobs. Workers are less likely to be poached the higher pay is and more likely to be poached otherwise. Lastly, starting wages solely explain the duration of E to NE matches; i.e. those formed by a worker who just executed a job-to-job transition and who will become nonemployed once the current match ends. For these matches, initial and current macroeconomic conditions are insignificant. In the data, workers in these matches are older and more educated, which are attributes consistent with these matches being more immune to the cycle. Returning to the examples from the beginning, the current results provide a new interpretation for why vacancy creation falls in recessions and rises in expansions, similar to Hall (2017). If in recessions new hires are tilted toward NE to NE type matches, then the empirical results suggest vacancy creation should fall: the surplus of these matches has a high discount rate (i.e. they are of short expected duration), and importantly, starting wages do not completely internalize this discount. Conversely, if in expansions new hires are disproportionately E to E (or E to NE) type matches, then the current results reconcile why vacancy creation rises: the surplus of these types of matches has a lower discount rate (i.e. they are of longer expected duration). Additionally, starting wages internalize changes in the discount, suggesting firms respond to higher poaching activity in expansions by raising wages. This paper is related to several strands of the empirical macro labor literature. The empirical analysis is closely related to the work of Bowlus (1995) who finds that matches starting in recessions are of shorter duration and relates this to match quality being low in recessions and high in booms. This paper complements that work by considering the importance of the worker s pre- and 3

5 post-employment status for accounting for cyclical variation in match duration and controlling for individual fixed heterogeneity. Distinguishing matches by prior and future employment status of the worker is necessary for finding the pro-cyclical duration of some matches versus the counter-cyclicality of others. This distinction also highlights that the link between duration and quality is obscured by the possibility of on-the-job search. 1 Accounting for individual fixed heterogeneity is critical for the finding that match quality is not solely internalized by initial wages. Also related is the more recent empirical work of Kahn (2008) and Kahn and McEntarfer (2014). Using firm-level data, Kahn (2008) finds that employment relationships that start in recessions are short-lived. However, once firm heterogeneity is taken into account this effect is reversed, suggesting the importance of firm differences in explaining differences in job duration over the cycle. This paper complements that work by focusing on the worker side. Using U.S. matched employer-employee data, Kahn and McEntarfer (2014) find that downturns hinder the progression of workers toward higher paying firms. This paper is complementary to theirs as it shows how the duration of matches formed by workers who executed a job-to-job transition varies over the cycle and depends on whether the worker will become nonemployed or re-employed once the current match ends. Additionally, Oreopoulos, von Wachter, and Heisz (2012) and Altonji, Kahn, and Speer (2016) find large and persistent earnings declines for new graduates entering the labor market during a recession. 2 They find that the effect is strongest for the least skilled workers, reminiscent of a cleansing effect. Relative to these papers, the current paper is silent about long-term individual consequences of entering the labor market in a recession versus a boom. However, this paper s finding that NE to NE matches are more likely to end in recessions (i.e. are cleansed) and are formed by less educated workers is consistent with their evidence. The next section discusses the estimation strategy and the data used for 1 Related to this point is the work of Barlevy (2002). 2 See also, Kahn (2010) who finds similar results when using the NLSY. 4

6 the empirical analysis. Section 2 presents the baseline estimation results, while Section 3 shows how many of the main results are not accounted by differences in starting pay. Finally, Section 4 concludes. 1 Estimation and data description This section first outlines the estimation procedure used to measure cyclical variation in match duration and highlights the importance of looking both at the pre- and post-employment status of the worker. Next, a description of the data is provided, followed by a discussion of the representativeness of the sample. 1.1 Estimation strategy A proportional hazard model with time-varying regressors is estimated to empirically assess the cyclicality of match duration. This type of model is chosen as it allows for the inclusion of censored observations in the estimation without imposing additional assumptions on the hazard function. Specifically, the hazard takes the form: λ(t X(t)) = λ 0 (t) exp(β X(t)) (1) Here λ 0 (τ) represents the baseline hazard of a job ending at time t; β is a coefficient vector to be estimated, and X(t) is a vector of individual and aggregate characteristics at time t. Over the duration of the job spell, these characteristics are either constant (e.g. race, education, and cyclical conditions at the start of the job) or time-varying (e.g. labor market experience, and current labor market measures). Analysis time begins when the match is first observed and ends when the match dissolves (or is no longer observed). Following Bowlus (1995), cyclical conditions in the labor market are proxied by the national unemployment rate. Like Bowlus (1995), the vector X(t) includes: the national unemployment rate when the match begins u 0, the current unemployment rate u t, and the square of the current unemployment 5

7 rate u 2 t. Unlike Bowlus (1995), X(t) also includes an interaction term between the initial and current unemployment rates u 0 u t, individual fixed-effects, and year fixed-effects. Demographics, education, and experience are controlled for using indicators for race, educational attainment, and a cubic in labor market experience. Key to the analysis is the coefficient on the initial unemployment rate u 0. A positive coefficient on u 0 suggests matches starting in expansions are expected to be of longer duration. Next, the current unemployment rate, u t, captures how current conditions affect hazard rates independent of when the match begins. Like Bowlus (1995) the current unemployment rate is introduced in a non-linear manner, u 2 t, to help distinguish between the pro-cyclicality of voluntary switches and the counter-cyclicality of involuntary separations or layoffs. Meanwhile, the interaction term, u 0 u t, captures how initial conditions and current conditions interact. Including this variable follows the implications of Menzio and Shi (2011) and Lise and Robin (2016): some low quality matches are formed in expasions only to be destroyed as soon as conditions deteriorate. Beyond including measures of cyclical conditions and observable individual characteristics, Equation 1 is estimated using individual fixed-effects. Controlling for fixed-effects alleviates biases arising from unobserved fixed heterogeneity. Additionally, each individual s spells are weighted by the inverse of the number of spells observed for them normalized by the number of survey waves to which they respond. 3 the likelihood estimation of Equation 1. This allows each individual to contribute equally in Year-fixed effects capture the unbalanced nature of expansions versus recessions. Expansions are more frequent and longer lasting than recessions, and by construction more matches will be observed in expansions. Not accounting for this unbalanced nature will tend to bias the estimated effects toward what occurs in expansions. 3 Normalizing by the number of survey waves helps distinguish between individuals who report few long duration jobs lasting over several years versus individuals who report few jobs because of attrition. 6

8 The proposed sampling scheme uses as much data as possible. Alternatively, one could use only the first two observed spells for each individual, as suggested by Chamberlain (1985), or use one randomly chosen spell as suggested by Bowlus (1995). These sampling schemes, in general, will lead to less efficient estimation. 4 Lastly, because the main explanatory variables include non-linear terms in the current unemployment rate and the interaction between initial and current conditions, the analysis in the next section provides illustrative examples of how estimates of the hazard rate in Equation 1 translate into changes in median duration given different initial conditions and at different states of the cycle. Throughout the analysis, starting in a boom (bust) represents the effect of u 0 being one standard deviation below (above) its mean. Similarly, currently being in a boom (bust) represents the effect of u t being one standard deviation below (above) its mean. Then, for example, starting in a boom but currently facing deteriorating conditions reflects a situation where u 0 is one standard deviation is below its mean, while u t is one standard deviation above its mean. 1.2 Match quality and the importance of pre- and postemployment status of the worker The estimation strategy deliberately focuses on cyclical changes in match duration without making direct reference to match quality. 5 Models like Jovanovic (1979) imply a positive relationship between match quality and duration, as longer duration suggests the match meets or exceeds a (potentially time-varying) reservation productivity threshold. However, other features of the labor market, like on-the-job search, may distort this positive relationship. 6 4 Allison (1996) finds that under conditions of moderate censoring (e.g. the majority of individuals experience at least two events) the fixed-effects estimator is nearly always better than the conventional partial likelihood estimator when applied to repeated events with unobserved heterogeneity. 5 This section is motivated by suggestions from an anonymous referee. 6 Barlevy (2002) emphasizes that fewer job-to-job transitions in recessions will tend to reduce average match quality (i.e. a sullying effect), but makes no explicit link to job duration. 7

9 To illustrate this point, consider two matches of the same quality, one observed during an expansion and another during a recession. Moreover, assume the quality is high enough so that the match is not endogenously destroyed in a recession or boom. Under this setup, one would infer from the long duration of these matches that they are high quality ones. On-the-job search, however, provides another reason for matches to dissolve. Importantly, during an expansion a worker may be more likely to move to a better job through on-the-job search, as more vacancies increase the contact rate of the worker with other potential employers. In the hypothetical example, now the possibility of on-the-job search will shorten the duration of match observed during an expansion, but lengthen the duration of the match observed during a recession even though both are of the same underlying quality. This example highlights the potential pitfalls of equating duration with quality, but also suggests what other information may be useful in measuring the cyclicality of duration. Specifically, in the above example the pre- and post-match employment outcomes of the worker are key. For example, short duration matches that end with the worker executing a job-to-job transition to another job should be treated separately from short duration matches that end with the worker without a job. As such, an important component of the empirical analysis focuses on how the cyclicality of match duration depends on whether or not the worker was previously employed and whether or not the worker will be employed following the dissolution of the current match. 1.3 Data The data used in this study come from the National Longitudinal Survey of Youth (NLSY), survey years 1979 through The NLSY is a nationally representative sample of 12,686 young men and women who were years old when first interviewed in Interviews were conducted annually through 1994 and biennially thereafter. The NLSY has important advantages over other surveys for studying job duration. Compared to address based surveys, such as the Current Population 8

10 Survey (CPS), individuals do not drop out of the sample following a change in geographical location, which may be highly correlated with job duration. During each interview participants report information for up to five jobs that can be linked across consecutive interviews. Thus, the NLSY s format allows for more consistent construction of duration variables when compared to surveys such as the Panel Study of Income Dynamics (PSID). 7 Importantly, the NLSY should capture short matches in between interview dates. Lastly, the NLSY has a much longer panel dimension in comparison to other longitudinal surveys such as the Survey of Income and Program Participation (SIPP), which only follows individuals for four years. Following Bowlus (1995), the sample is restricted to males from the crosssectional samples and only job spells that start when the individual is at least 18 years old and not in school are included. Individuals must work at least 15 hours per week. Spells that end prior to 1979 or lasting less than a month are dropped. Unlike Bowlus (1995), all spells of an individual are considered, rather than restricting the sample to a single random spell per individual. Hence, the sample not only covers more years but also more information per individual. To construct the main sample of jobs and their respective durations, data from the Employer Roster Survey is used. Using the variables that contain the start and stop dates for each job report, the start of the match is defined as the week when the job is first recorded. The end of the match is defined as the week when the job is last linked. 8 Gaps within the duration of a match are ignored. This distinguishes this paper s measure of job duration versus tenure on the job. The sample is restricted to primary jobs. Specifically, spells that are contained within the duration of another job are dropped. Job-to-job transitions are defined as whenever the worker was non-employed for at most two weeks in between jobs and the previous job ended because of a quit. With this in mind, 7 See Brown and Light (1992) for an in depth discussion of the issues when measuring job tenure in the PSID. 8 The duration of a job is defined as right-censored whenever the individual is currently working at the job during the time of the interview when the match is last reported. 9

11 NE matches are defined as those formed with previously nonemployed workers and who were laid off from their last job. E matches are defined as those formed workers who performed a job-to-job transition to reach the current job. NE to NE matches are those where the worker was previously nonemployed (and laid off from their last job) and will become nonemployed (via laid off) once the current match ends. NE to E matches are those where the worker was previously nonemployed (and laid off) and will execute a job-to-job transition once the current match ends. Lastly, E to E matches are those where the worker executed a job-to-job transition to land the current job and will execute another one once the current match ends. All jobs satisfying the previous requirements are used in the estimation. The resulting sample consists of 5,676 spells from 1,905 individuals. Table 1 presents summary statistics for the main sample and by prior and future employment status of the worker. Note, this sample excludes individuals with only one spell as fixed-effects cannot be estimated with such individuals. It also excludes spells where the reason the previous (or current) job ended is unknown. 9 Comparing columns of Table 1 reveals significant heterogeneity and underscores the importance of looking at the worker s employment history. For example, NE to NE (and NE to E) matches are shorter, while E to NE matches are considerably longer. Additionally, workers in NE to NE matches are less educated and are more likely to be a minority. In contrast, workers in E to E matches are more educated and more likely to be white. Lastly, workers in E to NE matches are older and more educated. Also worth noting are the differences in initial conditions each type of match faces. NE to NE (and NE to E) matches start when the unemployment rate is higher than average, while E to NE (and E to E) matches start when the unemployment rate is lower than average, consistent with the fact that these matches start from a job-to-job transition. Furthermore, matches also face different sequences of current conditions. While NE to NE (and E to NE) matches face on average lower unemployment rates during their existence, NE 9 Section B.2 shows the main results are robust to relaxing this last restriction. 10

12 Table 1. Summary statistics (1) (2) (3) (4) (5) All NE to NE NE to E E to NE E to E Median job duration (in months) Avg. age when job starts Avg. unemployment rate when job starts (u 0 ) Avg. current unemployment rate (u t ) % non-white 20.10% 27.58% 19.88% 17.68% 15.69% % less than high school 19.24% 25.83% 19.88% 14.15% 17.06% % high school 48.15% 50.49% 51.18% 49.59% 43.54% % some college 17.46% 13.82% 18.13% 18.21% 19.62% % college or more 15.15% 9.86% 10.81% 18.06% 19.78% # of spells 5,676 1, ,329 1,835 Note: Source NLSY men in cross-sectional samples. to E (and E to E) matches face higher unemployment rates. 1.4 Representativeness It is important to note that the analysis sample is not representative of the entire U.S. population as it follows men of a particular cohort. In particular, this cohort is young in the late 80s and early 90s, which are relatively tranquil periods, and more established in their career paths in the 2000s, which includes two recessions including the Great Recession. Since job mobility declines with age, results based on this NLSY sample may imply less cyclical variation in job duration compared to a more representative sample of individuals over the same period. 2 Empirical results This section presents the main empirical results of the paper. The first subsection shows expansions are associated with longer match duration and this is particularly true for matches formed by workers who were previously nonemployed. The second subsection offers a more nuanced picture once separating matches by the worker s pre- and post-employment status. 11

13 2.1 Baseline results Table 2 presents the results from estimating the hazard in Equation 1 and show the importance of initial conditions for explaining variation in job duration. The standard errors in parentheses in Table 2 are clustered by time as this is the level of variation of the key explanatory variables (e.g. the initial and current unemployment rates). 10 The first column shows the initial national unemployment rate, u 0, has a positive and statistically significant effect on the hazard rate. In other words, matches starting in booms are of longer expected duration. Using a smaller sample and narrower time frame, Bowlus (1995) estimates a coefficient on the initial national unemployment rate of , which is very similar to the coefficient presented in Column 1. Importantly, though, Column 1 does not account for individual unobserved heterogeneity in spite of using multiple spells per individual. Column 2 adds worker fixed-effects to the estimation and shows that accounting for unobserved heterogeneity across individuals increases the size and significance of the coefficient on u 0. Accounting for this heterogeneity switches the estimated sign on the interaction term, though the coefficient is not statistically significant. The negative sign on the interaction term suggests any positive effect from starting a match in a boom is boosted as aggregate conditions improve. Table 3 presents how these coefficients translate into changes in median duration to illustrate their quantitative significance. Recall, starting in a boom (bust) represents the effect of u 0 being one standard deviation below (above) its mean. Similarly, currently being in a boom (bust) represents the effect of u t being one standard deviation below (above) its mean. Note the first row of Table 3 presents what median duration is estimated to be under normal conditions (i.e. both the initial and current unemployment rates at their respective means). Focusing on Column 1 of Table 3, which is based on the estimates from Column 2 of Table 2, shows that initial conditions have a pro-cyclical effect on 10 Section B.1 shows the main results do not change when clustering by job spell, which accounts for correlation across observations of the same spell. Note that allowing for personlevel fixed-effects controls for correlation across spells of the same individual. 12

14 Table 2. Hazard estimates: NLSY sample (1) (2) (3) (4) B95 All NE E u * *** ** (0.026) (0.035) (0.082) (0.050) u t (0.073) (0.083) (0.169) (0.119) u 2 t (0.016) (0.021) (0.043) (0.033) u 0 u t * (0.015) (0.020) (0.044) (0.028) Worker FE NO YES YES YES No. of obs. 199, ,833 67, ,111 Note: u 0 denotes the unemployment rate at the time when the match begins. u t denotes the time-varying current unemployment rate. u 0 u t denotes the interaction between the initial and current unemployment rate. Standard errors are clustered by time and appear in parentheses. Regressors not reported: cubic in experience, year fixed-effects, and indicators for race, less than high school education, some college, and college graduate (or more). +,,, indicate statistical significance at 10%, 5%, 1%, and 0.1% levels. duration. The second row shows that median duration rises to 33 months (32% increase) if a match begins a boom. The next row illustrates the importance of current conditions and their interaction with initial conditions. Recall, the negative sign on the interaction term suggests worsening (improving) economic conditions dampen (boost) the positive effect of starting in a boom. On the other hand, the negative coefficient on u t suggests worsening (improving) current conditions increase (reduce) duration. Comparing the second and third rows of this table shows that both of these effects cancel each other out leaving duration unchanged. Indeed, while the median duration of a match that starts in a boom and is currently in a boom is 33 months, the duration of a match that starts in a boom and is currently in a bust is also 33 months. The previous estimates suggest booms are associated with longer duration, but do not provide evidence whether prior employment status matters. Indeed, the measured pro-cyclical effect that initial conditions have on duration may be arising from marginal matches that are only created in booms with previously nonemployed workers, which are then subsequently destroyed in recessions. 13

15 Table 3. Estimated change in median duration (in months) over the cycle overall and by pre-employment status (1) (2) (3) All NE E normal conditions start boom, current boom start boom, current bust Note: results for Column 1-3 are based on the estimates from Columns 2-4 in Table 2, respectively. To test this hypothesis, Columns 3 and 4 of Table 2 consider matches formed with previously nonemployed workers (NE matches) versus those who switched between jobs (E matches), respectively. The results in Columns 3 and 4 suggest the pro-cyclical effect of initial conditions on duration is mostly due to marginal matches that start in booms and end in recessions. The positive and statistically significant coefficient on u 0 in Column 3 suggests booms are associated with longer job duration particularly NE matches. Additionally, the interaction term in Column 3 is negative and significant, suggesting the benefits of starting in a boom are dampened as current conditions deteriorate. In contrast, neither initial nor current conditions tend to explain variation in the hazard rate of E type matches. The second and third columns of Table 3 show that the duration of NE matches is more cyclically sensitive compared to E matches. The first row shows that under normal conditions NE matches are shorter than E matches (13 versus 47 months). However, the second row reveals the greater cyclicality: while the median duration of an NE match more than doubles if it begins in a boom, the duration of an E match rises by only 15%. Lastly, the third row shows that changes in contemporaneous conditions have stronger effects on NE matches and this critically depends on the estimated sign on u t. For NE matches a deterioration in current conditions decreases duration on net: the median duration of an NE match that started in a boom and is currently in a bust is estimated at 12 months, which is shorter 14

16 than the duration of an NE match that started in a boom and is currently in a boom (30 months) and shorter than an NE match that started under normal conditions (13 months). This is the result of two reinforcing mechanisms. First, a deterioration in current conditions dampens duration given the estimated positive coefficient on u t in Column 3 of Table 2. Second, since the match started in a boom, a deterioration in current conditions drags down duration given the negative coefficient on the interaction term u 0 u t. Overall, the duration of NE matches falls drastically if they start in booms and are currently in busts. In contrast, a deterioration in current conditions has a more nuanced effect on E matches. The median duration of a match that is currently in a bust is 51 months, which is shorter than the duration of a match currently in a boom (54 months), but longer than an E match under normal conditions (47 months). This is the result of two opposing mechanisms. First, a deterioration in current conditions boosts duration given the estimated negative coefficient on u t in Column 4 of Table 2. Second, since the match started in a boom, a deterioration in current conditions drags down duration given the negative coefficient on the interaction term u 0 u t. 2.2 Results by previous and future employment status The previous results suggest starting in a boom is associated with longer duration, but they do not provide evidence whether future employment status of the worker helps predict duration. For example, that for E matches a deterioration in current conditions increases duration (i.e. the negative coefficient on u t ) may be capturing the fact that job-to-job transitions fall in recessions, which limits poaching activity and increases duration. To address this issue, Table 4 presents hazard estimates by the pre- and post-employment status of the worker. Columns 1 and 2 of this table look at matches where the worker was previously nonemployed, but distinguish between matches where the worker becomes nonemployed (NE to NE matches) versus transitions to another job upon dissolution of the current match (NE 15

17 to E matches). Columns 3 and 4 present equivalent estimates, but consider matches where the worker was previously employed and either becomes nonemployed (E to NE matches) or transitions to another job once the current match ends (E to E matches), respectively. The key takeaway from Table 4 is that both prior and future employment status matters when measuring the cyclicality of match duration. Holding prior employment status constant but varying future employment status (e.g. comparing Columns 1 and 2), results in coefficients with opposite signs. Similarly, holding future employment status constant but varying prior employment status (e.g. comparing Columns 1 and 3), also results in coefficients with opposite signs. For matches with a previously nonemployed worker, Comparing Columns 1 and 2 of Table 4 to Column 3 of Table 2 highlights the importance of looking at post-employment status. In Table 4, the estimated coefficient on u 0 is positive and statistically significant for NE to NE matches (Column 1), but negative and insignificant for NE to E matches (Column 2). In other words, the positive coefficient on u 0 seen in Column 3 of Table 2 is due to matches where the worker returns to nonemployment once the current match ends. Additionally, comparing Columns 1 and 2 of Table 4 to Column 3 of Table 2 clarifies the how initial and current conditions interact when looking at NE matches. Indeed, the estimated coefficient on the interaction term, u 0 u t, is negative and significant (like what is observed in Column 3 of Table 2) for NE to NE matches, but positive and significant for NE to E matches. Overall, the results in Columns 1 and 2 suggest different characterizations for the duration of NE to NE versus NE to E matches. NE to NE matches last longer if they start in expansions and are negatively affected by a deterioration in contemporaneous conditions. This finding is consistent with these matches having low surplus; they create positive surplus in an expansion when aggregate productivity is high, but negative surplus once aggregate productivity declines. Recall, these matches are formed by less educated workers. On the contrary, the results in Column 2, though less precise, suggest NE to E matches are shorter if they begin in expansions and are positively affected by 16

18 a deterioration in current conditions. This is consistent with the job-to-job transition rate rising in expansions, which reduces duration at the onset of the match, and falling in recessions, which increases expected duration based on current conditions. Table 4. Hazard estimates by pre- and post-employment status: NLSY sample (1) (2) (3) (4) NE to NE NE to E E to NE E to E u *** * (0.122) (0.217) (0.341) (0.077) u t (0.230) (0.451) (0.666) (0.149) u 2 t *** * (0.057) (0.133) (0.256) (0.046) u 0 u t *** * (0.059) (0.126) (0.231) (0.047) Worker FE YES YES YES YES No. of obs. 42,861 24,861 79,392 52,719 Note: u 0 denotes the unemployment rate at the time when the match begins. u t denotes the time-varying current unemployment rate. u 0 u t denotes the interaction between the initial and current unemployment rate. Standard errors are clustered by time and appear in parentheses. Column 1 restricts the estimation to spells where the individuals was previously non-employed and becomes non-employed upon match dissolution. Column 2 is estimated spells where the individuals was previously non-employed and but becomes employed in another match upon dissolution of the match in question. Column 3 restricts the estimation to spells where the individual was employed prior to the current match and becomes non-employed upon match dissolution. Column 4 uses spells where the individual was previously employed and becomes employed in another match once the current match ends. Regressors not reported: cubic in experience, year fixed-effects, and indicators for race, less than high school education, some college, and college graduate (or more). +,,, indicate statistical significance at 10%, 5%, 1%, and 0.1% levels. To see this characterization more clearly, the first and second columns of Table 5 present the median duration implications of the previous estimates. The first row shows that under normal conditions NE to NE matches are slightly shorter than NE to E matches. The second row illustrates the opposite effects that initial conditions have on both types of matches. While the duration of NE to NE matches rises if they start in booms, the duration of NE to E matches falls. Next, the third row of this table highlights how current conditions differentially affect each type of match. For NE to NE matches that start in a boom, a deterioration in current conditions reduces median duration 17

19 (from 113 to 13 months) compared to a similar match that started in a boom and is currently in a boom. This occurs because the duration dampening effect of the negative interaction term u 0 u t in Column 1 of Table 4 offsets the duration boosting effect of the negative coefficient on u t. In contrast, for NE to E matches that start in a boom, a deterioration in current conditions boosts duration (from 9 to 31 months) compared to a similar match that starts in a boom and is currently in a boom. This follows because the duration boosting effect of the positive interaction term u 0 u t in Column 2 of Table 4 offsets the duration dampening effect of the positive coefficient on u t. Focusing next on matches with a previously employed worker, Columns 3 and 4 in Table 4 reveal that the observed pro-cyclical duration of these matches is driven by instances where the worker transits to another job following match dissolution (i.e. E to E matches). To see this point, note the coefficient on u 0 is negative and insignificant for E to NE matches (Column 3), but positive and significant for E to E matches (Column 4). The fact that none of the estimated coefficients in Column 3 are significant is perhaps not surprising given the long duration of E to NE matches. Recall, the results from Table 1 show median duration of these matches is nearly six years and these matches are formed by individuals who are older and more educated than average. In contrast, E to E matches are considerably shorter with median duration of 22 months. The last two columns of Table 5 illustrate the quantitative effects of the estimated coefficients for E to NE and E to E matches. The second row of Columns 3 and 4 shows that both median duration of E to NE and E to E matches rises if they begin in booms and are currently in booms. Importantly, though, the rise in duration of E to NE matches is due to good current conditions (i.e. the positive coefficient on u t and negative coefficient on u 0 u t ), which completely offsets the modest counter-cyclicality coming from good initial conditions (i.e. the negative coefficient on u 0 ). To see this last point more clearly, the third row of Column 3 shows that a deterioration in current conditions reduces the median duration of E to NE matches from 409 to 112 months, again suggesting that the main driving 18

20 Table 5. Estimated change in median duration (in months) over the cycle by preand post-employment status (1) (2) (3) (4) NE to NE NE to E E to NE E to E normal conditions start boom, current boom start boom, current bust Note: results are based on estimates from Columns 1-4 in Table 4. force behind changes in the duration of these matches are changes in current conditions. In contrast, the third row of Column 4 shows that a deterioration in current conditions boosts the median duration of E to E matches from 24 to 27 months. This occurs mainly because of the negative estimated coefficient on u t as seen in Column 4 of Table 4, since the interaction term u 0 u t is quantitatively small. 2.3 Summary To close, the results from this section highlight the importance of initial and current conditions, the interaction between the two, and looking both at preand post-employment outcomes of the worker for understanding cyclical variation in match duration. The main results are summarized as follows. First, the duration of NE to NE matches rises if they begin booms and falls as current conditions deteriorate. Second, the duration of NE to E matches is notably different; duration falls if they begin in booms, but rises as current conditions deteriorate. Third, the duration of E to E matches rises if they begin in expansions and continues to rise as current conditions worsen. Lastly, though the estimates are insignificant, the duration of E to NE matches is mostly dictated by current conditions: better current conditions boost duration and worse current conditions dampen it. 19

21 3 Are starting wages important? Overall, the previous results provide evidence of cyclical variation in job duration, and that the direction of the cyclicality varies considerably by pre- and post-employment status of the worker. This section asks whether this variation is captured by starting wages and finds that many of the results from the previous section are not internalized by cyclical changes in starting pay. 11 This finding is important as it hints to why vacancy creation falls in recessions: firms do not entirely offset the high discount rate (i.e. short duration) of matches formed in recessions by reducing wages, which in turn reduces the present value of forming a match in a recession. 3.1 Baseline results To show starting wages do not internalize differences in expected duration over the cycle, Table 6 repeats the estimation of Equation 1 but includes initial (log) real wages in the regression. The first column of this table replicates the Bowlus (1995) finding that initial wages make the estimated coefficient on the initial unemployment rate, u 0, decline in magnitude and become insignificant. However, the second column reveals that once individual fixed-heterogeneity is taken into account initial wages still matter, but so does the initial unemployment rate. The estimated coefficient is now 0.08, which is not much different from what is reported in Table 2. Lastly, the coefficient on initial wages, lnw 0, suggests higher starting pay boosts expected duration, while lower starting pay reduces it. To gain insights into whether the results in Column 2 of Table 6 are quantitatively different from those reported in the previous section, the first column in Table 7 presents how median duration varies over the cycle given the current set of estimates. The first row shows that median duration under normal macroeconomic conditions and given an average starting wage is 24 months. The second row shows that median duration rises to 42 months if the match starts in a boom, which is larger than the increase from 25 to 33 months im- 11 See Pissarides (2009) for a summary of the evidence on the cyclicality of wages. 20

22 Table 6. Hazard estimates with starting wages: NLSY sample (1) (2) (3) (4) B95 All NE E u ** ** (0.028) (0.037) (0.086) (0.053) u t (0.076) (0.095) (0.194) (0.128) u 2 t (0.018) (0.023) (0.047) (0.033) u 0 u t ** (0.015) (0.021) (0.045) (0.030) lnw *** *** *** *** (0.051) (0.076) (0.131) (0.133) Worker FE NO YES YES YES No. of obs. 190, ,817 64, ,153 Note: u 0 denotes the unemployment rate at the time when the match begins. u t denotes the time-varying current unemployment rate. u 0 u t denotes the interaction between the initial and current unemployment rate. lnw 0 denotes the initial log real wage. Standard errors are clustered by time and appear in parentheses. Columns 1 and 2 are estimated with all spells. Column 3 restricts the estimation to spells where the individual was previously not employed and was laid off from her most recent job. Column 4 only uses spells where the individual was previously employed and quit her most recent job. Regressors not reported: cubic in experience, year fixed-effects, and indicators for race, less than high school education, some college, and college graduate (or more). +,,, indicate statistical significance at 10%, 5%, 1%, and 0.1% levels. plied by the results from the previous section that do not control for starting wages. Lastly, the third row shows that a deterioration in current conditions dampens duration. Median duration falls from 42 to 26 months when current conditions turn unfavorable. This contrasts with the results in the previous section that show no change when current conditions deteriorate. This finding is because of the different estimated signs on u t : the estimate is negative in Table 2, but positive in Table 6. Hence, a deterioration in current conditions by itself dampens duration once starting wages are taken into account. The last row in Table 7 shows the large quantitative effect that changes in initial wages have on duration. In this scenario a low w 0 represents a 20% 21

23 Table 7. Estimated change in median duration over the cycle when starting wages are included (1) (2) (3) All NE E normal conditions start boom, current boom start boom, current bust low w 0, start boom, current boom Note: results for Columns 1-3 are based on the estimates from Columns 2-4, respectively, in Table 6. decrease in starting wages relative to the cross-sectional mean. 12 The key takeaway from this row is that lower initial wages essentially offset any of the benefits from starting a match in an expansion. For example, if a match starts in a boom, with an average starting wage, and current conditions are favorable, then median duration is 42 months. Holding initial and current macroeconomic conditions constant, but decreasing the starting wage is enough to reduce median duration to 30 months, nearly a 30% decrease. Next, looking at the remaining columns of Table 6 confirms that many of the results from Section 2.1 by prior employment status are robust to the inclusion of starting wages into the hazard equation. For NE matches (Column 3), the coefficient on u 0 remains positive and statistically significant. Additionally, controlling for initial wages increases the size and significance of the coefficient on the interaction term u 0 u t. Lastly, comparing the coefficients on lnw 0 in Columns 3 and 4 suggests initial wages have a stronger effect on the hazard of E matches. To see this more clearly, Columns 2 and 3 of Table 7 show the quantitative implications of the estimates from Columns 3 and 4 of Table 6. The second row confirms that the median duration of both types of matches rises in expansions, though the duration of NE matches rises by more in both absolute 12 This change is roughly half a cross-sectional standard deviation. 22

24 and percentage terms. Next, the third row shows that a deterioration in current conditions reduces the duration of both NE and E matches, though the duration of NE matches falls by more in both absolute and percentage terms. Finally, the last row shows that low initial wages more than offset any of the benefits of starting a match in an expansion, with the effect being stronger for E type matches. For example, if an E match starts in a boom, with an average starting wage, and is currently in a boom, then median duration is 48 months. However, if the same match starts with a low initial wage then median duration falls to 31 months, or a 35% decline. In contrast, the same experiment on an NE type match results in duration falling from 38 to 32 months, or a 16% decline. Overall, the results in Table 6 and Table 7 illustrate that while starting wages have large quantitative effects on expected duration, initial and current macroeconomic conditions still help explain variation in job duration, particularly for matches with previously nonemployed workers. In contrast, for matches with previously employed workers, starting wages appear to be the main predictor of expected duration since initial and current macroeconomic conditions are insignificant. 23

25 3.2 Results by previous and future employment status This section mirrors the analysis from Section 2.2 and finds that many of those results are also robust to the inclusion of starting wages in the hazard regression. In particular, even once controlling for starting wages, initial and current macroeconomic conditions still help explain cyclical differences in the duration of NE to NE and NE to E matches. However, initial and current macroeconomic conditions are statistically insignificant predictors of the duration of E to NE and E to E matches once accounting for starting wages. To see these points more clearly, Table 8 presents estimates by pre- and post-employment status when initial (log) real wages are included in the hazard equation. As before, Columns 1 and 2 of this table examine matches where the worker was previously nonemployed, but distinguish between those where the worker becomes nonemployed (NE to NE matches) versus transitions to another job upon dissolution of the current match (NE to E matches). Meanwhile, Columns 3 and 4 present similar estimates, but consider matches where the worker was previously employed (E to NE matches and E to E matches, respectively). The estimates in Column 1 confirm the characterization of NE to NE matches from Section 2.2. The coefficients on the initial unemployment rate (u 0 ), the square of the current unemployment rate (u 2 t ), and the interaction between initial and current conditions (u 0 u t ), are all statistically significant and of the same sign as in Table 4. Additionally, these estimates reveal that initial wages are a significant predictor of duration. Meanwhile, the estimates in Column 2 reiterate the cyclical differences in the duration of NE to E versus NE to NE matches. The coefficient on u 0 remains negative and statistically insignificant. However, the inclusion of initial wages in the hazard regression increases the size and significance of both the quadratic term of the current unemployment rate (u 2 t ), and the interaction between initial and current conditions (u 0 u t ), relative to the equivalent estimates in Table 4. Lastly, initial wages also have a statistically significant effect on duration. Table 9 highlights the similarities between these results and those in Ta- 24