Dynamics of Displaced Worker Earnings and Aggregate Labor Market Fluctuations

Transcription

1 Dynamics of Displaced Worker Earnings and Aggregate Labor Market Fluctuations Pawel Michal Krolikowski University of Michigan, Ann Arbor September 29, 2012 Preliminary and incomplete: Please do not cite without permission Abstract Previous literature documents large and persistent earnings losses of displaced workers. This paper proposes a sophisticated search and matching model that explains the robust empirical findings pertaining to displaced workers. The model explains persistent earnings losses after displacement with poor match-quality among first jobs in conjunction with a job ladder. Persistent low quality matches in post-displacement employment relationships explain serially correlated displacement spells, which previous empirical studies have found to be an important explanation for the persistence of earnings losses. The model sheds light on the empirically inconclusive movement of earnings prior to displacement. The experience of displaced workers seems to contribute little to the amplification and propagation of productivity shocks at the aggregate level. Nevertheless, recessions have a temporary cleansing effect, and within a year cause average match-quality to fall. JEL Codes: D83, E24, J62, J64. Key words: displacement, earnings, search, match-quality, propagation. Contact information: University of Michigan Department of Economics, 611 Tappan Street, Ann Arbor, MI pawelk@umich.edu. Special thanks go to my committee: Michael W. L. Elsby, Dmitriy Stolyarov, Matthew D. Shapiro and Brian P. McCall, for their constant encouragement, support, critique and commitment to my work. This project would not be what it is without my committee s dedication. I would like to thank University of Michigan s Rackham Graduate School for funding via the Predoctoral Fellowship Program and University of Michigan s Economics Department for funding through the Robert V. Roosa Dissertation Fellowship. I would also like to thank Christopher L. House for his input and intuition throughout this project. I would like to thank Ruediger Bachmann and Alexander Ludwig for featuring my work at the poster session of the 2010 Cologne Workshop on Macroeconomics, and Kenneth L. Judd for enabling me to present my work at the poster session of the 2010 Institute on Computational Economics hosted by the University of Chicago. I want to thank my friends and colleagues Andrew H. McCallum, Daniel P. Murphy, David Ratner, Gabe Ehrlich, David Knapp, and Ryan Nunn for their insights and feedback as I worked through the details of this project, as well as William F. Lincoln, Italo Gutierrez, Ana Mocanu and Andrew Goodman-Bacon for their help at early stages of this work. Finally, I would like to thank all the Michigan Macro-International Lunch and Labor Seminar participants for their comments. I am responsible for any remaining errors.

2 1 Introduction Displacements affect many participants of the United States labor market. 1 According to the Displaced Worker Supplement to the Current Population Survey (CPS), 6.9 million workers with at least three years of tenure experienced job loss due to layoff from 2007 to 2009 (BLS (2010)). An additional 8.5 million persons were displaced from jobs they had held for less than 3 years. As another example, Davis and von Wachter (2011) find that 16 percent of prime-aged males with three or more years of job tenure experienced a job displacement event from 1980 to In conjunction with the high incidence of displacement, there now exists a long and distinguished literature documenting the earnings experience of displaced workers. Although the point estimates differ, economists typically find that displaced workers with three to six years of tenure incur large earnings losses in the year of displacement, and that these losses persist for many years following the displacement event. I present details on this extended literature in Appendix (A), and I point the reader to work by Jacobson et al. (1993), von Wachter et al. (2007) and Schmieder et al. (2009). As an example, Davis and von Wachter (2011) find that prior to displacement, on average, workers experience a slight increase in real earnings: in the year prior to displacement earnings are two percent above the annual earnings of the control group. The authors show that at the time of displacement, real earnings fall sharply, and even twenty years after the time of displacement annual earnings are 15 percent below pre-displacement earnings. The presence of these large and persistent earnings losses for displaced workers has been documented time and time again. The model presented in this paper explains the magnitude and persistence of earnings losses among displaced workers. The first part of the explanation coincides with work by Stevens (1997) who finds that multiple additional job losses are an important part of a workers post-displacement experiences and in the years following an initial displacement serially correlated displacements explain much of the persistence and magnitude in lowered earnings. The model presented here mimics this finding and displays serially correlated displacement spells. The model captures the following intuition: compared to their job prior to displacement, workers might not be as well matched in their first job coming out of unemployment. This poor fit results in tentative new employment relationships as small downward movements in productivity (demand) can cause these relationships to terminate. The second part of the explanation is the presence of a substantial job ladder through the presence of (persistent) match-specific human capital. The job ladder captures the idea that workers suit some jobs better than other jobs, and it takes time for workers to find the jobs for which they are well suited. In conjunction with poor quality matches among first jobs, the job ladder prolongs the earnings recovery path after displacement as unemployed workers enter poor employment relationships and search for better matches while employed. 1 Economists typically define displacement as job loss that results from a firm decision, and not a worker s decision. For example, reasons for job loss that are classified as displacement include layoff, slack work/demand, a plant closing or a position/shift abolished. With administrative data, where reason for job loss is unavailable, researchers often use mass layoffs to identify displacements. 2

3 This paper also sheds some light on movements in earnings prior to displacement. In the baseline estimation, I follow the empirical literature and analyze workers with at least three years of tenure at the time of displacement. This specification implies that agents do not experience any displacements in a three-year window prior to separation. Since the model features idiosyncratic productivity (demand) and endogenous separations, this means that earnings tend to rise prior to displacement, relative to a control, as the three-year tenure requirement restricts the analysis to employment relationships that perform better than average. The empirical literature appears inconclusive on the time-path of earnings prior to displacement, but, as an example, Davis and von Wachter (2011) find that workers experience a slight increase in real earnings prior to displacement. Without conditioning on tenure, the model implies that earnings prior to displacement should fall, due to the serially correlated displacements highlighted in the previous paragraph. This serial correlation implies that agents tend to experience above-average rates of separation prior to displacement. This implies that their average match-quality tends to fall below average, and hence displaced workers experience falling earnings prior to displacement. With a partial equilibrium model that features persistent earnings losses of displaced workers, I use the steady state features of the model to assess the implications of the experience of displaced workers for the cyclical dynamics of job flows. The model provides a novel way to calibrate the match-quality process, using the earnings time-path of displaced workers. Along with an otherwise standard calibration the theory delivers the procyclicality of the job-finding rate for both the unemployed and the employed, as well as the countercyclicality of the employment to unemployment transition rate in the United States. The model also delivers some persistence in unemployment, although the partial equilibrium mechanisms seem to contribute little to the amplification and propagation of aggregate labor productivity shocks. The literature has rarely applied search models to the experience of displaced workers. Davis and von Wachter (2011) come closest to the work presented here. They show that a standard Mortensen-Pissarides model, and a slightly more sophisticated model found in Burgess and Turon (2010), cannot explain the extent of losses observed in the data. The model presented in this paper differs from Burgess and Turon (2010) in a crucial way: the unemployed enter work towards the bottom of the job ladder and workers in first jobs face higher hazard rates of separation into unemployment than workers in established employment relationships. This serial correlation causes cycles of job loss and can significantly raise the costs of one displacement. Although the model presented by Burgess and Turon (2010) also has low idiosyncratic productivity among first jobs, the hazard rate into unemployment is the same for all workers, whereas the model presented here features very fragile new employment relationships. In addition to differing hazard rates into unemployment post displacement, the model presented here features persistent match-quality. This captures the idea that individuals rarely move from being poorly suited for a job to being very well suited for a job. This job-search process usually takes time and the quality of job offers tends to cluster around an individual s current match-quality. Persistent match-quality significantly slows down the recovery of earnings of displaced workers, and provides an improvement over the 3

4 model of Burgess and Turon (2010). Pries (2004) stands as another closely related paper. The work presented here differs in two ways. First, I present a quantitative exercise that matches well the empirical results on displaced worker earnings and provides calibrated values for parameters of interest, whereas Pries (2004) provides only a qualitative discussion about displaced worker earnings. Second, my story hinges on a job ladder and on-the-job search, both of which Pries (2004) omits. Hence, my model can speak to issues, like employer-to-employer (E-E) flows before and after separations, and the extent to which job switches account for the recovery in earnings post displacement. Pries model cannot speak to these dimensions of the data. In particular, my model suggests decreased E-E flows prior to displacement as workers get trapped in failing firms, as well as increased E-E flows after displacement as workers climb the job ladder in search for a better suited job. In Section (5) I present evidence from the Panel Study of Income Dynamics (PSID) that weakly corroborates the post-displacement E-E flows suggested by the model, but refutes the E-E flows prior to separation. After using the partial equilibrium model to capture the time-path of displaced worker earnings, I next turn to the implications of the model for the aggregate dynamics of vacancies and unemployment. I close the model by introducing the vacancy-posting decision of the firm, which in turn depends on the steady state distribution of idiosyncratic productivity (demand) and match-quality among employed workers. This distribution exhibits slowmoving behavior following a negative aggregate productivity shock as low quality matches are destroyed, and it takes workers time to find new jobs and slowly climb up the job ladder. The implications of this slow moving distribution are relatively limited for aggregate dynamics. Although average match-quality and idiosyncratic productivity (demand) move over the cycle, they have little affect on the expected payoff from meeting an employed worker and therefore relatively little influence on the aggregate vacancy rate and unemployment. These results dovetail with results found in Barlevy (2002), who finds that in a similar model to the one described in this paper, a 72 percent downward, permanent shock to aggregate productivity induces movements in average match-quality of less than one percent. I organize the rest of the paper as follows. Section (2) outlines the quantitative framework and provides some intuition for the dynamics of the model. Section (3) outlines the solution to the theoretical model, and discusses the calibration and identification of key model parameters. The main results of the paper regarding the earnings of displaced workers appear in Section (4). Section (5) discusses external validity of the model. Section (6) presents a discussion about the inadequacy of alternative versions of the model. Section (7) closes the partial equilibrium model by introducing the aggregate vacancy creation condition. Section (8) presents aggregate implications of the partial equilibrium model for aggregate transitions. Section (9) concludes. 4

5 2 The Model 2.1 Model Introduction This paper uses the search and matching framework developed by Mortensen, Diamond and Pissarides. This model extends Mortensen and Pissarides (1994) and Pissarides (2000) by incorporating match specific quality with endogenous job destruction. In other words, two quantities characterize every match: the quality of the match and idiosyncratic productivity (demand). Although the model features undirected on-the-job search, it does not feature intensity of search or search costs. The model features privately efficient separations, which means that worker and firm act to maximize their joint value, as well as exogenous separations. In this model all unemployed workers are equivalent. Their idiosyncratic productivity (demand) does not follow them into unemployment. I assume linear utility (risk-neutrality) throughout. 2.2 Setup This paper presents a partial equilibrium search model. Workers look for jobs and firms post vacancies to attract workers. I assume that each firm only has one vacancy and thus can hire at most one worker. Unemployed workers receive utility from leisure and encounter vacancies at an exogenous probability p U. Employed workers receive a flow payment w and produce a flow output. Employed workers participate in on-the-job search and contact vacancies at a different probability p E. 2 All employer-employee matches are characterized by two state variables: match-quality denoted by y, and an idiosyncratic component denoted by x, which can be interpreted as either productivity or demand. The product of x and y provides the flow output of the match. When an unemployed worker contacts a firm, the match draws an initial, non-stochastic, match-quality equal to y 0. 3 Match-quality remains constant within a job. If the worker encounters a firm via on-the-job search, match-quality is drawn from distribution F y (y y). All initial idiosyncratic productivities (demands) are fixed at a deterministic value, x 0, and then exhibit persistence within a match and evolve according to F x (x x). The model would deliver very similar qualitative results with identically and independently distributed idiosyncratic productivity as in Mortensen and Pissarides (1994). I choose this process for idiosyncratic productivity for calibration purposes. Setting x to x 0 in all new matches follows Mortensen and Pissarides (1994). 4 2 The differing job contact probabilities on and off the job may result from differing levels of search intensity exhibited by the employed and the unemployed. I abstract from the reason behind this difference in the model. 3 Setting match-quality to y 0 in all new matches makes the work focus on what Doeringer and Piore (1971) call port-of-entry jobs. More recently, Martins et al. (2010) similarly focus on jobs that repeatedly show new hires. Assuming the same match-quality in all new jobs suggests there exist a set of entry-level jobs that involve the same amount of job-specific human capital. On a more technical note, with variation in initial y, unemployed individuals reject offers and thus the job finding rate is not equal to the unemployment-toemployment rate. The data do not help us distinguish unemployed individuals who have rejected petty offers and those who have not received any offers. I take the stance that all unemployment is frictional. 4 Alternative versions of the model presented a tension between matching the unemployment-toemployment rate consistent with the size of the earnings dip in the year of displacement and the employmentto-unemployment rate consistent with recovery. This results from a large number of offers evaluating to 5

6 In this model the match-quality, y, can be interpreted as human capital. y provides a mean productivity level and x provides some variance around this mean productivity. Over time on-the-job search results in offers to the employed with match-quality drawn from y F y (y y). This induces a job-ladder which agents climb over time as they acquire human capital. This can be interpreted as finding more suitable jobs within the same firm (promotions) or simply learning specific skills and moving onto jobs that are better suited for the worker. Notice that match-quality exhibits persistence. This captures the idea that individuals rarely move from poor match-qualities to excellent match-qualities. Climbing the job usually takes time and the quality of job offers tends to cluster around your current match-quality. I must note here that the persistence in match-quality is admittedly reduced form. One interpretation may be that y incorporates both general and job-specific human capital, thus exhibiting persistence from job to job. However, the fact that all first jobs start at match-quality equal to y 0 implies that agents lose all their general human capital during unemployment. Although there does exist a literature documenting a reduction in general human capital during unemployment (see for example, Ljungqvist and Sargent (2008) and citations within), the loss of all general human capital seems unrealistic. The idiosyncratic component delivers endogenous flows into unemployment; when the idiosyncratic random variable gets low enough, the worker and the firm decide to part ways. The worker prefers to flow into unemployment and search for a new vacancy, and the firm wants to let the worker go and find a new worker from the pool of searchers. This endogenous separation occurs when the surplus from the match dips below zero. Involuntary separations on either side of the market do not occur in this model. Whenever there exists positive surplus in a match, the worker and firm can negotiate a wage both parties find agreeable. Whenever the surplus from a match is exhausted, firm and worker both want to terminate the current employment relationship. 2.3 Timing of Events within a Period Within each period, events among unemployed workers unfold according to the following timing. At the outset of a period firms post vacancies to recruit unemployed workers and workers look for jobs. When workers contact open vacancies the idiosyncratic productivity (demand) level and match-quality are realized and the worker and firm decide whether to consummate the match. New matches wait until next period to produce. For established employment relationships, or among employed workers, the timing for workers and firms is as follows. First, firm and worker bargain over the wage. Second, production occurs and the firm pays the worker. Third, the idiosyncratic component undergoes a shock. Finally, workers receive outside offers with some probability. If an employed worker receives a favorable outside offer, he moves to the poaching firm. If an employed worker receives no outside offer, below b (the value of leisure) because the variance of the initial x is large (agents prefers to wait because they might draw a really good x). This implies that the variance of the initial x is less than the variance of the x once a match is consummated. Here I take a particularly stark version where x = x 0. This allows the unemployment-to-employment rate to be high and the employment-to-unemployment rate to be high. This assumption suggests that workers start with the same level of productivity (demand) in all jobs. 6

7 the firm and the employee decide to preserve the match or separate (separation may occur because of negative surplus or the exogenous separation shock). 2.4 Bargaining At the beginning of each period, every worker-firm pair bargains over the wage, w(x, y), that the firm pays the worker for production. I assume a standard generalized Nash bargaining rule over the total surplus of the match, so that the worker receives a fraction β of the total surplus and the firm receives a fraction (1 β) of the total match surplus. 2.5 Intuition for the Partial Equilibrium Model Before I discuss the formal model equations, I want to provide a simple description of the model dynamics and give the reader intuition for the mechanics of the model. The model delivers a slow recovery in earnings post-displacement for three reasons. First, immediately post-displacement, the calibrated model suggests that workers take jobs with lower matchqualities, compared to their pre-displacement jobs, and the average match-quality among employed workers. Second, in conjunction with a low match quality among first jobs, the job ladder effect introduces persistence in earnings; it takes time for employed workers to find good quality matches. Third, low post-displacement match-qualities mean that newly created jobs are likely close to the job destruction threshold. This makes it more likely that these matches will be destroyed, resulting in multiple displacements and serial unemployment. This serial unemployment effect dovetails with work by Stevens (1997) who finds that multiple job losses are an important explanation for the persistence of earnings losses. Prior to separation the model provides the following intuition about earnings. Without any tenure requirements, earnings tend to fall even prior to displacement due to the serial correlation in displacements outlined in the previous paragraph. This serial correlation implies that workers tend to experience above-average rates of separation prior to displacement. This implies that their average match-quality tends to fall below average, as the calibrated value of match-quality in first jobs, y 0, lies below the average match-quality in the economy. Due to this decline in average match-quality prior to displacement, average earnings tend to fall even prior to displacement. Although the empirical evidence on the movements of earnings prior to displacement remain inconclusive, some displaced workers experience declining earnings prior to displacement (see, for example, Jacobson et al. (1993)). In order to follow the empirical literature, in the baseline results I estimate the earnings losses associated with displacement using workers who have at least three years of tenure at the time of displacement. This treatment group, therefore, experiences no displacements during the three years prior to their displacement. Since the model features idiosyncratic productivity (demand) and endogenous separations, this implies that the average idiosyncratic component for this restricted sample must exceed the average idiosyncratic component for the average worker. This implies that earnings tend to rise prior to displacement, relative to a control group, as the three-year tenure requirement restricts the analysis to employment relationships that perform better than average. 7

8 2.6 Bellman Equations Joint Value of a Match Define the continuation value of employed workers and firms as W (x, y, w) and J(x, y, w) respectively. Let U be the continuation value of unemployed workers. Free entry into vacancies implies that the firm s value of a vacancy is zero. For notational convenience, define the joint value as the sum of the value of a match to the worker and the firm: V (x, y) = W (x, y, w) + J(x, y, w) Notice that w does not change the joint value of a match V ; it merely determines the allocation of the joint value between worker and firm. A higher w implies that the worker receives more of the match value. The joint value function satisfies: V (x, y) = x y + δ (1 p E ) (1 p }{{} s ) }{{} No outside No + δ p }{{} E (1 p s ) Outside offer + δp s U offer separation shock max{u, V (x, y) }{{} Match continues max{v (x, y), U} df }{{} x (x x) Match continues or terminates, V (x 0, y )} }{{} Worker moves to poaching firm }df x (x x)df y (y y) where p E is the probability of contacting an outside firm, p s is the probability of an exogenous separation shock, δ stands for the discount factor and β represents the bargaining power of the worker. The flow payoff from the match equals x y, the product of productivity and matchquality. Every period a shock to productivity arrives. In the event of no outside job offer (occurs with probability 1 p E ), and no exogenous separations shock (occurs with probability p s ) the employment relationship either continues with joint value V (x, y), or a separation occurs. In the event of separation, the worker receives continuation value U and the firm is left with nothing (remember that the value of a vacancy is zero in equilibrium), which makes the joint continuation value U. Notice that the V (x, y) term captures renegotiation: the employment relationship continues, but a new wage, w, divides the surplus differently. When a productivity shock occurs and the worker contacts an outside firm, three things can happen. 5 First, the outside offer could be worse than the current match, and the productivity shock makes the current match unbearable. This causes a separation, which leaves the worker with U and the firm with zero. Second, the current employment relationship continues with V (x, y). Third, the outside offer induces renegotiation and the worker leaves the current firm (V (x 0, y ) exceeds V (x, y)). In this case, I assume that the workers use unemployment as their outside offer and the continuation value is simply V (x 0, y ), the joint value at the new firm. In particular, I assume that workers cannot use their current offer as a starting point for bargaining. 5 Note that separation shocks occur prior to outside offers so that receiving a separation shock implies workers move into unemployment whether they have an outside offer or not. 8 (1)

9 Finally, if the match receives an exogenous separation shock, the worker flows into unemployment and the match value equals U Value of Work to the Employee The value of work satisfies the following equation: W (x, y) = w + δ(1 p E )(1 p s ) + δp E (1 p s ) + δp s U max{u, W (x, y), W (x 0, y )} }{{} Worker moves to unemployment, stays at current firm, or goes to new firm max{w (x, y), U} }{{} Match continues or terminates df x (x x)df y (y y) df x (x x) (2) The value of work is a function of two state variables: the idiosyncratic productivity x and the match-quality y. The first term on the right-hand side is the flow payoff from working, which is the current wage: w. Note that I assume a linear utility function (risk-neutrality). The second term on the right-hand side corresponds to the event of no outside job offer. Since I assume the productivity shock arrives every period, I need to consider what happens when the productivity changes. If W (x, y) > U the relationship is still viable (there is positive surplus), and the worker and firm immediately re-bargain to obtain the new wage. If V (x, y) < U the relationship is no longer viable. The employment partnership comes to an end. The third term on the right-hand side corresponds to the worker contacting an outside firm (and a productivity shock). The worker leaves the current employment relationship only if the match value of the new match exceeds the value at the current firm. The timing here is important: the value from the current match and the value at the poaching firm are compared after the shock to current productivity (demand) arrives. In this case, the worker chooses between two options: unemployment and working at the new firm. In the latter case, the worker bargains with the outside firm using unemployment as his outside option. In the event that the match value at the current firm exceeds both the value of unemployment and and the match value at the outside firm, the worker remains at the current firm receiving value W (x, y). If U > max{w (x, y), W (x x 0, y )), the surplus at the current firm and the outside offer falls below zero, and so the worker moves to unemployment receiving continuation value U. Finally, if the match receives an exogenous separation shock, the worker flows into unemployment and the continuation value equals U. 9

10 Given the previous definitions, the value of a filled job to the firm is simply: J(x, y, w) = V (x, y) W (x, y, w) (3) Value of Unemployment The value of unemployment satisfies: U = b + δ(1 p U )U + δp U max{u + β[v (x 0, y 0 ) U], U} }{{} Match consummates or not (4) where p U is the probability of making a contact with a vacancy for unemployed workers. The first term captures the flow payoff from unemployment: b. The second term corresponds to no outside job offer. In this case the worker simply remains unemployed. The third term corresponds to an outside job offer. In this case the worker chooses between working at the contacting firm and unemployment. The payoff from working at the firm is the outside option, U, plus β times the surplus, which is [V (x 0, y 0 ) U]. 2.7 Solving the Partial Equilibrium Model I derive one central functional equation in the surplus from a match, S(x, y). Appendix (B) provides the details of this derivation. Here I simply present the result: S(x, y) = x y + δ (1 p E ) (1 p }{{} s ) max{0, S(x, y) }df }{{}}{{} x (x x) No outside No Match + δp E (1 p s ) offer separation shock max{0, S(x, y) }{{} Match [b + δp U β max{0, S(x 0, y 0 )}] }{{} Worker s outside option continues continues, S(x 0, y ) }{{} Worker moves to poaching firm }df x (x x)df y (y y) The first part of the right hand side is the flow payoff from a match, x y. The second piece captures the event of no outside job offer, no exogenous separation shock and the continuation value of the match. In this case, the match either comes to an end or the match continues with the new idiosyncratic productivity (demand). The third piece captures the event of the worker receiving an outside offer and potentially moving to the poaching firm. When the worker moves to the poaching firm he uses unemployment as a threat point. The final piece is the outside option of an employed worker: he forgoes the value of unemployment, b, and the possibility of finding a job at a new firm with surplus S(x 0, y 0 ) and receiving β of this surplus. Notice that equation (5) is a functional equation in only S(x, y). Value function iteration yields a close approximation to this function, denoted by Ŝ(x, y). (5) 10

11 Assuming a Nash bargain for the wage pins down the equilibrium wage equation as a function of (x, y). I present the details in Appendix (B), and here I state the result: w(x, y) = βs(x, y) + [b + δp U β max{0, S(x 0, y 0 )}] }{{} δ (1 p E ) (1 p }{{} s ) β }{{} No outside No offer separation shock δp E (1 p s )β Worker s outside option max{0, S(x, y) }df }{{} x (x x) Match max{0, S(x, y) }{{} Match continues continues, S(x 0, y ) }{{} Worker moves to poaching firm }df x (x x)df y (y y) (6) The worker receives a fraction β of the total surplus along with the value of his outside option, which incorporates the possibility of finding a new job. The wage must also reflect the possible changes in future idiosyncratic productivity, the possibility of poaching by an outside firm, and the event of an exogenous separation. 3 Estimation Strategy 3.1 Processes for x and y I set the model period length to one month. I assume that idiosyncratic productivity starts out at a fixed and deterministic level x 0 in all matches, and then within the match follows a log AR(1) process: ln x = ρ x ln x + ɛ x (7) where ɛ x N (0, σ 2 ɛ x ). Match-quality follows the following distribution: ln y 0 for jobs out of unemployment (U E) ln y = ln y if no job change ρ y ln y + ɛ y if changes jobs (E E) where ɛ y N (0, σ 2 ɛ y ). In other words, match-quality remains constant within a job, and is distributed according to a log AR(1) process when a worker meets a new firm. In the first job coming out of unemployment, match-quality is set to y Estimation Methodology I refer the reader to Appendix (C.1) for details regarding value function iteration. Given the optimal decisions of workers and firms, the model generates simulated data at a monthly frequency. In particular, I simulate 15,000 agents for 480 months (40 years). To remove the effects of initial conditions, I simulate the model for 1280 months and then discard the 11

12 first 800 months of the sample. This simulation provides a time-path of wages and annual earnings, as well as an employment history. I compare the earnings of displaced workers in the model-generated data with the earnings of displaced workers observed in live data. I calibrate the parameters of the model using simulated method of moments. Certain key moments summarize the simulated data; among others, these moments include gross flows between employment and unemployment, establishment-level productivity processes, and the time-path of earnings for displaced workers. Simulated method of moments estimation minimizes the distance between the summary statistics of the simulated data and the summary statistics of real data. Specifically, if θ represents the vector of structural parameters, ĝ represents the moments of the actual data, and g(θ) represents the moments of simulated data then the simulated minimum distance estimator is defined as ˆθ = arg min L(θ) = arg min[g(θ) ĝ] [g(θ) ĝ] (8) θ θ Here g(θ) represents a non-linear transformation of the structural parameters by the model, as well as an analysis of the simulated data to achieve a moment that is comparable to the moment from the real data. Some of the targeted moments are parameters of an auxiliary model, such as coefficients from an estimated equation using the observed data. In this sense, the approach here implements a technique called indirect inference. 3.3 Calibration/Identification In this section I present the key moments of the data and discuss the identification strategy. When discussing the identification strategy I describe how changes in parameters effect moments of the simulated data. Due to the high non-linearity of the model, no one moment pins down identification of a parameter. Nevertheless elucidating the identification of key components of the model is a worthwhile exercise. Table (1) summarizes the baseline parameters. Table (2) shows that the model gets close to matching the calibration targets. Parameter Meaning Value Reason (θ) (ˆθ) ρ x Productivity persistence 0.99 (M) Persistence of plant productivity σ ɛx Std. dev. of productivity 0.04 Std. dev. of plant productivity ρ y Match-quality persistence 0.93 (M) Recovery of displacement earnings σ ɛy Std. dev. of match-quality 0.15 On-impact dip of annual earnings p E Contact probability (E) Employer-to-Employer flow probability p U Contact probability (U) 0.45 Aggregate job-finding probability b Value of leisure 0.71 APL Hall and Milgrom(2008) x 0 Starting productivity 1.13 E[x match] Employment-to-Unemployment flow probability p s Exogenous separation probability Pre-displacement earnings y 0 Match-quality in first jobs E[y] 1 Normalization Table 1: Calibrated Model Parameters The x y process represents movements in total factor productivity. Foster et al. (2008) use the Census of Manufacturers to estimate the annual persistence in establishment-level 12

13 persistence to be I choose ρ x to match this observed persistence in establishmentlevel productivity. More explicitly, I choose ρ x and then estimate the following equation via OLS using the simulated data: x t+1 y t+1 = β 0 + β 1 x t y t + ξ t+1 (9) where x y represents TFP in my model, and Foster et al. (2008) find that ˆβ 1 [0.75, 0.8]. β 1 depends positively on ρ x, because raising ρ x increases the persistence of the idiosyncratic productivity process, which in turn increases the observed persistence of idiosyncratic total factor productivity in the simulated data. The variance of ɛ x is set to match the standard deviation of plant-level productivity. Foster et al. (2008) estimate the standard deviation for plant level productivity (in logs) to be between 0.21 and 0.26 (table (1) of their paper). They take the log of the product of productivity at all plants, and calculate the standard deviation. I follow an equivalent procedure with the simulated and take the log of the product of x and y among all matches and calculate the standard deviation. In the calibration, this value is a little higher than in the data. The starting idiosyncratic productivity for unemployed individuals, x 0, is targeted to generate the employment to unemployment (E-U) instantaneous transition rate found in the United States gross flows data. As I raise x 0, unemployment becomes more and more appealing because the first job coming out of unemployment has higher productivity. This induces a larger fraction of the employed to flow into unemployment every period. Elsby et al. (2010) find the layoff inflow rate is around 1.5 percent (table 9). This is similar to the E-U transition rate, which is around 1.7 percent (table 10). Since most displacements occur through no fault of the worker using the layoff inflow rate is an appropriate target. The calibrated value of x 0 lies above the steady state expectation of x, which implies, on average, a downward drift in productivity after match consummation. Further, this suggests that agents sometimes switch to jobs with lower match qualities in order to reset the idiosyncratic productivity to x 0. Intuitively, this suggests that sometimes workers leave behind good quality matches and move to jobs with very high idiosyncratic productivity. Nevertheless, on average, workers match-qualities and wages rise over their lifetime. The standard deviation of match-quality is difficult to quantify in the data. The model provides a convenient way of calibrating this parameter: the on-impact dip in earnings resulting from displacement. Increasing the dispersion in y implies that agents on average move further up the job ladder, and have more earnings to lose, when they experience a displacement. This increases the on-impact dip in earnings resulting from displacements. The resulting estimate of σ ɛy seems reasonable. As an alternative, in a very similar model to the one presented here, Low et al. (2010) estimate the standard deviation of match-quality at My estimate lies at around 70 percent of this value. I target the trajectory of the post-displacement earnings recovery using the persistence of match-quality. In particular, raising the dependence of outside offers on current offers implies 13

14 that workers move slowly up the job ladder and therefore post-displacement earnings tend to recover slowly. As an extreme example, suppose that match-quality followed a random walk. Then, in expectation, worker s match-quality would move up very slowly as the current match-quality would serve as the best predictor of the worker s match-quality at an outside offer. With this process for match-quality, after being displaced, a worker would move up the job ladder very slowly, rarely encountering offers better than his current offer. This would significantly slow down the recovery of earnings. I use p E to generate the observed E-E transition rate. This relationship is quite obvious. Raising the number of contacts employed workers have with outside firms raises the probability that workers experience E-E switches. Intuitively, this implies that E-E flows in the model are monotonically increasing in p E. Fallick and Fleischman (2004) use data from the basic monthly Current Population Survey (CPS) from January 1994 to December They find that an average of 2.6 percent of employed persons change employers each month. More recently Nagypal (2008) finds similar results using the CPS: 2.88 percent for all observations and 2.5 percent for all observations of age She finds using the SIPP that the E-E rate is about 25 percent lower than in the CPS: 2.2 percent. I target a monthly E-E transition rate of 2.6 percent. The contact probability for the unemployed, p U, is determined by targeting the aggregate job-finding probability. Increasing the job-contact rate means that unemployed workers experience more frequent contacts and since workers accept all first offers in this model, the unemployment-to-employment (U-E) probability rises. Following Shimer (2005) I target a monthly job-finding probability of I choose p s, the exogenous separation rate, to target a slight increase in earnings for hightenured workers prior to displacement. There appears to be no empirical consensus on the movement of earnings prior to displacement. Some studies, such as Jacobson et al. (1993) or von Wachter et al. (2007), find a large reduction in earnings even prior to displacement. Other studies, such as Davis and von Wachter (2011) or Couch and Placzek (2010), find a rise in earnings prior to displacement. The calibration of p s does not make a significant difference to the results that I present in the rest of this paper, so I decide to target the most recent, comprehensive study on displaced worker earnings, Davis and von Wachter (2011), using Social Security Administration data in the United States. As a comparison, with only exogenous separations (p s = 0.015) in the model there would be no movement, on average, in earnings prior to displacement because exogenous separations occur randomly. Alternatively, if all the displacements in the model were endogenous (p s = 0) then, conditioning on three years of tenure at the time of displacement, earnings will rise in the three years prior to displacement. This follow because match-quality is fixed due to the tenure restriction and idiosyncratic productivity rises as the agents do not experience any separations in three years and therefore their idiosyncratic productivity must rise relative to the control group. 14

15 Moments in the data Data Model (ĝ) (g(ˆθ)) Pesistence of Foster et al.(2008): plant productivity (A) 0.58 (A) Annual std. dev. of Foster et al.(2008): plant productivity (logs) Recovery of post- Davis and von Wachter(2011): displacement earnings 20% 20% On-impact dip of Davis and von Wachter(2011): annual earnings 30% 28% Employer-to- Fallick and employer flows Fleischman(2004): Job-finding rate Shimer(2005): Value of leisure Hall and Milgrom(2008): 0.71 AP L 0.71 AP L Employment-to- Elsby et al. (2010): Unemployment flows Pre-displacement Davis and von Wachter(2011): rise in earnings 3% 2% Table 2: Calibration Targets I set b to be consistent with the value found in Hall and Milgrom (2008): 0.71 of average productivity of labor (APL). 6 Previous literature, such as Hagedorn and Manovskii (2008), show that that the calibration of this parameter is important for the volatility of unemployment and the job finding rate predicted by the model. The emphasis of this paper is not the cyclical behavior of unemployment and vacancies over the business cycle, so the calibration of this parameter is less crucial. The value found in Hall and Milgrom (2008) serves as a benchmark. I calibrate the bargaining power of the worker, β, to 0.5. This serves as a benchmark, and is close to the calibrated figure used by Elsby and Michaels (2010). The literature provides little guidance in terms of how to calibrate this parameter. In the partial equilibrium context, I cannot use the Hosios (1990) result and impose efficiency by equating the worker s bargaining power with the elasticity of the matching function with respect to the unemployment rate. The results presented below are robust to the choice of β. Finally, I choose r to target a five percent annual interested rate. 6 Calculating the average labor productivity analytically involves integrating x y against the joint density of (x, y) among matches. This joint distribution differs from F x and F y because of selection in the model. Solving for this joint distribution involves equating outflow and inflows from regions of this joint distribution, much like in Burdett and Moretensen (1998) and solving explicitly for this distribution involves iterating on functional equations, which involve the value functions of this model. Hence, solving numerically for this distribution makes the computational burden of the algorithm overwhelming. To avoid this, I simply set b to be a fraction of the unconditional average labor productivity and then find after simulating the data because with the simulated data I can simply compute the ALP by averaging x y over all workers and all time periods. b ALP 15

16 4 Results 4.1 Earnings Dynamics Around Displacement To compare the simulated data to the observed data, I aggregate the simulated monthly wage data into annual earnings data and estimate an equivalent equation to the one found in Davis and von Wachter (2011): 7 e it = α i + 20 k= 6 D k itδ k + ɛ it (10) where the outcome variable e it is annual earnings of individual i in year t, α i represent individual fixed effects, and D k it are dummy variables equal to one in the worker s kth year before or after his displacement, and zero otherwise. Davis and von Wachter (2011) estimate: e y it = αy i + γy t + ē y i λy t + βx it + 20 k= 6 D k itδ k + u y it (11) where the new variables γ y t are coefficients on calender-year fixed effects, X it is a quartic polynomial in the age of worker i at year t, the error u y it represents random factors, and λy t allows annual earnings increments to differ by a worker s initial level of earnings, calculated using the years y 5 to y 1 (ē y i ). My model does not feature time variation that needs to be controlled by using time fixed effects hence I omit γ y t and λ y t from the estimated equation. As expected, including these variables in the regression has no impact on the estimated coefficients. Furthermore, I omit the y superscript because all years in my model are identical, so I fix y at an arbitrary year. As in Davis and von Wachter (2011), I restrict my sample to individuals who have at least three years of tenure at the time of displacement. Figure (1) presents a comparison between the results from my model and the results from Davis and von Wachter (2011). 8 The model captures the time-path of earnings so well that its implied movements in earnings are difficult to differentiate from the results based on real data. It seems that the search model outlined in this paper can account for the time-path of displaced worker earnings. in particular, the model outlined in this paper suggests that luck can account for all the earnings losses associated with displacement. 7 A non-trivially different specification can be found in Stevens (1997) or Jacobson et al. (1993). These studies focus on the earnings losses around the first displacement. In a short accompanying paper (Krolikowski (2012)) I explicitly show that the distributed lag models initially implemented in Jacobson et al. (1993), and used in the literature for the last 20 years, measure the losses associated with displacement relative to a time when the treated workers experience no displacements, i.e. prior to their first displacement. It comes as no surprise that workers who intermittently experience displacement have persistently lower earnings than they had when they did not experience any job loss. In alternate versions of this model, including versions with no persistence in match-quality, the model was able to deliver losses using these alternate specifications, but could not target the losses from the specification found in Davis and von Wachter (2011), which measures the earnings losses with respect to any displacement, not just the first displacement. 8 As in Davis and von Wachter (2011) I plot the estimated δ k coefficients, which are earnings losses relative to a non-displaced control group with the same tenure requirement as the displaced treatment group, relative to the average pre-displacement earnings of the treatment group in the 4 years prior to displacement. 16

17 Figure 1: Annual Earnings Losses: Model vs. Data The model captures the slight movement in earnings prior to displacement well, except for the downward movement in earnings in years -6, -5 and -4. On impact the model predicts well the losses in annual earnings: around 30 percent. Additionally, the model captures the movements in earnings post-displacement very well. After 20 years the model delivers similar losses to those found in the data. The downward movement in earnings in years -6, -5 and -4 results from serial correlation in displacements, which implies that workers displaced in time period 0 experience displacements before this time, and this lowers the average match-quality and therefore average earnings. This downward movement in earnings also results from the fact that, relative to a control group, those displaced in time period 0 experience fewer job offers while employed. This captures the notion that workers that experience displacement get trapped at failing firms without an outside offer. Loss in match-quality results in the on-impact dip in earnings, as workers fall from higher rungs of the job ladder, to a low job rung in their first job out of unemployment. On-impact, idiosyncratic productivity rises because x 0 > E[x match]. Earnings fall slightly in the year following displacement because some workers get displaced late in the 0 year and so have a substantial amount of earnings in the year of displacement. Since it takes unemployed workers time to find jobs, and y 0 < E[y match] so that first jobs pay very little, in the year immediately following displacement workers may actually experience a small dip in earnings. In addition to this timing issue, the high serial correlation in displacements implies that in the year following the investigated displacement, the worker may experience subsequent displacements which reduce his annual earnings even further. The slow recovery in earnings represents the slow move up the job ladder for recently displaced workers, which in turn manifests the persistence of match-quality and serial correlation in displacements. In particular, due to persistent match-quality agents receive outside offers which closely resemble their current job. Agents experience serially correlated displacements because match-quality remains low in first jobs and therefore only small movements in idiosyncratic productivity cause further displacements. 17