Online Appendix "Declining Desire to Work and Downward Trends in Unemployment and Participation" Regis Barnichon and Andrew Figura

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1 Online Appendix "Declining Desire o Work and Downward Trends in Unemploymen and Paricipaion" Regis Barnichon and Andrew Figura 1 Daa In he paper, we make use of wo ses of ransiion raes: he firs over beween he hree labor marke saes E, U, N, and he second over beween he four labor marke saes E, U, N w and N n. To measure individuals ransiion probabiliies p AB from labor force saus A {E, U, N} o labor force saus B {E, U, N} over , we use mached CPS micro daa from January 1976 hrough December 2010 and compue he number of workers moving from A o B each monh. We hen correc he measured ransiions for he 1994 CPS redesign as described below. To measure individuals ransiion probabiliies p AB from labor force saus A {E, U, N n, N w } o labor force saus B {E, N n, N w } over , we use mached CPS micro daa from January 1994 hrough December 2010 and compue he number of workers moving from A o B each monh. In boh cases, we hen correc he measured ransiions for ime-aggregaion bias Correcion for he 1994 CPS redesign When measuring ransiion probabiliies over , he 1994 redesign of he CPS (see e.g., Polivka and Miller, 1998) caused a disconinuiy in some of he ransiion probabiliies in he firs monh of 1994 (Abraham and Shimer, 2002). To adjus he series for he redesign, we proceed as follows. We sar from he monhly ransiion probabiliies obained from mached daa for each demographic group. We ake he pos-redesign ransiion probabiliies as he correc ones, and we correc he pre-94 value for he redesign. To do so, we esimae a VAR wih he six hazard ransiion probabiliies in logs esimaed over 1994m1-2010m12 and as used in Barnichon and Nekarda (2012), and we 1 We also implemened a correcion for margin error ha resrics he esimaes of worker flows o be consisen wih he evoluion of he corresponding labor marke socks, as in Poerba and Summers (1986). We did no correc he daa for classificaion error and spurious ransiions (Abowd and Zellner (1985), Poerba and Summers (1986)), because i is no clear how one should correc for such classificaion error in he CPS survey (Elsby, Hobijn and Sahin, 2013). Elsby e al. repor alernaive correcion mehods, and he secular rends appear broadly unchanged. 1

2 use he model backcas he 93m12 ransiion probabiliies 2 Wih hese 93m12 values in hand, we obain correced ransiion probabiliies over 1976m2-1993m12 by adding o he original probabiliy series he difference beween he original value in 93m12 and he inferred 93m12 value. By eliminaing he jumps in he ransiion probabiliies in 1993m12, we are assuming ha hese disconinuiies were solely caused by he CPS redesign. Thus, he validiy of our approach ress on he fac ha 1994m1 was no a monh wih large "rue" shocks o he ransiion probabiliies. We hink ha his is unlikely because here is no large movemens in he aggregae job finding rae and aggregae job separaion rae obained from duraion daa (Shimer, 2012 and Elsby, Michaels and Solon, 2009) ha do no suffer from hese disconinuiies. Indeed, hese auhors rea he 1994 disconinuiy by using daa from he firs and fifh roaion group, for which he unemploymen duraion measure (and hus heir ransiion probabiliy measures) was unaffeced by he redesign. Moreover, Abraham and Shimer (2002) used independen daa from he Census Employmen Survey o evaluae he effec of he CPS redesign on he average ransiion probabiliies from mached daa. They found ha only λ UN and λ NU were significanly affeced, and ha, afer correcion of hese disconinuiies (using he CES employmen-populaion raio), none of he ransiion probabiliies displayed large movemens in Correcion for ime-aggregaion bias The esimaed ransiion probabiliies suffer from ime-aggregaion bias because one can only observe ransiions a discree (in his case, monhly) inervals (Shimer, 2012). 3 We hus need o correc for ime-aggregaion bias for each demographic group. To do so, we use Shimer (2012) and Elsby e al. (2013) s mehod ha we generalize o a labor marke wih 4 saes wih {E, U, N w, N n } (employed, unemployed, "wan a job" nonparicipan, "no wan a job" nonparicipan). We consider a coninuous ime environmen in which daa are available only a discree daes. For {0, 1, 2...}, we refer o he inerval [, + 1[ as period. We assume ha he ransiion of workers across labor marke saes can be described by a (four-sae) Markov chain of order 1 wih he ransiion marix being consan during period. The number of employed E, unemployed U, "wan a job" nonparicipan N w and "no wan a job" nonparicipan N n 2 The number of lags were chosen o maximize ou-of-sample forecasing performances. A similar VAR is used in Barnichon and Nekarda (2012) o forecas he six flow raes. 3 Anoher issue is classificaion error (Abowd and Zellner, 1985 and Poerba and Summers, 1986). Alhough i is no clear wheher one should apply hese correcion mehods on he curren CPS survey, Elsby, Hobijn and Sahin (2013) ry differen correcion mehods, and he secular rends are broadly unchanged. 2

3 hen saisfies he sysem wih Y = P Y 1 (1) 1 p EU p EN w p EN n p UE p N w E p N n E p P EU 1 p UE p UNw p UNn p N w U p N n U = p EN w p UNw 1 p N wu p N we p N w N n p N n N w p EN n p UNn p N w N n 1 p N nu p N ne p N n N w where we omi he demographic group subscrip i for clariy of presenaion. To recover he hazard raes from he measured ransiion probabiliies (i.e., correc he ransiion probabiliies for ime-aggregaion bias), we need o recover he insananeous ransiion marix P in he coninuous ime sysem (2) Y = P Y 1 (3) The firs-order differenial equaion (3) has soluion Y = V Λ V 1 Y 1 wih V he marix of eigenvecors of P and Λ a diagonal marix wih he exponenial of he eigenvalues of P on he diagonal. Conrasing wih (1), i follows ha P has he same eigenvecors as P, so ha one can consruc P from P = V Λ V 1 wih V he marix of eigenvecors of P and Λ a diagonal marix wih he log of he eigenvalues of P on he diagonal. 2 Decomposiions of u, l and m This secion describes he decomposiion of (i) he unemploymen rae u, (ii) he paricipaion rae l, and (iii) he share of "wan a job" nonparicipans m. 2.1 Decomposiion of u and l We now describe he decomposiion of u and l underlying Figures 6-9 in he main ex. Denoing ω i = LF i LF he share of group i {1,.., K} in he labor force and Ω i = P op i P op he populaion share of group i, he aggregae unemploymen and paricipaion raes are given by u = l = K i=1 Ω i l i l u i (4) K Ω i l i i=1 3

4 The seady-sae unemploymen rae of group i, u i = U i LF i, saisfies where s i and f i are u i = u( { λ AB } ), A, B {E, U, N} = i s i s i + f i f i = λ UE i s i = λ EU i + λ UN i + λ EN i λ NE i λ NE +λ NU i λ NE i λ NU i i +λ NU i. (5) Similarly, he seady-sae labor force paricipaion rae of group i, l i = LF i P op i l i = l ({ λ AB }) i, A, B {E, U, N} s i + f i = s i + f i + λeu i λ UN i +λ UE i λ NE i λ EN i +λ NU i +λ UN i λ EN i saisfies. (6) The ideniies in (4) are funcions of he six hazard raes of each demographic group (he λ AB i s, A, B {E, U, N}, i {1,.., K}) and funcions of he populaion shares (Ω i, i {1,.., K}) of each group. By aking a Taylor expansion of he ideniies in (4) around he mean of he hazard raes of each demographic group i (λ AB i Eλ AB i ) and around he mean of he populaion share (Ω i Ω i EΩ i ) of each group, we can decompose he aggregae unemploymen rae u and labor force paricipaion rae l ino he conribuion of changes in demographics and he conribuions of movemens in each ransiion rae (sripped of demographic effecs): 4 wih du Ω = and du AB = { du = du Ω + du UE dl = dl Ω + dl UE + du UN + dl UN + du EU + dl EU + du EN + dl EN + dl NU + du NU + dl NE + du NE + ε l K β Ω i (Ω i Ω i ) capuring he conribuion of demographics i=1 K i=1 β AB i ( λ AB i + ε u λ AB ) i, A, B {E, U, N}, β AB i he coeffi ciens of he Taylor expansion, capuring he conribuion of λ AB, he ransiion rae from A o B o he unemploymen 4 By aking a Taylor expansion around he mean, insead of around an HP-filer rend or around las period s value as in Elsby e al. (2009) or Fujia and Ramey (2009), our decomposiion has he advanage of covering all frequencies and hence allows us o analyze low-frequency movemens (as well as cyclical movemens). The coeffi ciens of he Taylor expansion are available upon reques. To guaranee ha he approximaion remains good however, we ake a second-order approximaion, which performs exremely well, as we show in he nex secion. (7) 4

5 rae (holding he demographic srucure of he populaion consan). ε u is he Taylor approximaion error. Similar noaions apply o he decomposiion of he labor force paricipaion rae, bu subsiuing β AB i wih δ AB i, he coeffi ciens of he Taylor expansion of l i. Finally, by using equaion (3) in he main, we obain he effec of changes in he share of "wan a job" nonparicipans on unemploymen, du m du m = K i=1 β NU i [ (λ N w U i λ N ) n U λ NU ( i i λ N w E λ NE i i λ N ) ] n E i (m i m i ) (8) and a similar expression holds for dl m wih dl m = K i=1 [ δ NU i ( λ N w U i λ N ) ( n U i + δ NE i λ N w E i λ N )] n E i (mi m i ). (9) The upper panel of Figure 6 in he main ex shows du Ω, and he middle panel shows du m. The op panel of Figure 7 in he main ex shows du Ω, he second panel shows du NU + du NE, he hird panel shows du EU + du EN, and he fourh panel shows du UE + du UN. In he second panel, he dashed line repors du m. Figures 8 and 9 in he main ex are organized in a similar fashion for he aggregae paricipaion rae. Finally, we verify ha he second-order Taylor expansions behind he sock-flow decomposiions of unemploymen and paricipaion, equaion (7) do indeed capure, o a good approximaion, he movemens in unemploymen and paricipaion. Figure 1 plos, in plain black, he seady-sae unemploymen rae along wih, in dashed red, he unemploymen rae implied by (7). We can see ha our decomposiion does an excellen job a capuring unemploymen movemens. Similarly, Figure 2 plos in plain black, he seady-sae labor force paricipaion rae along wih, in dashed red, he labor force paricipaion rae implied by (7). Again, our decomposiion does an excellen job a capuring paricipaion movemens. 2.2 Decomposiion of m The accouning ideniy behind he sock-flow decomposiion of m is given by he seadysae of he sysem (1). Specifically, leing λ AB denoe he hazard rae of ransiing from sae A {E, U, N w, N n } o sae B {E, U, N w, N n }, in coninuous ime, we have U N w U N w = L N n N n }{{} ṡ } {{ } s λ EU λ EN w + P op λ EN n }{{} g 5

6 wih L = ( λ UE λ UNw λ UNn λ EU λ N wu λ EU λ N nu λ EU λ UNw λ EN w λ N wu λ N we λ N w N n λ EN w λ N n N w λ EN w λ UNn λ EN n λ N w N n λ EN n λ N nu λ N ne λ N n N w λ EN n The seady-sae of he sysem, s, is hen given by s = L 1 g. (10) From he expression for s, (10), we can hen define he seady-sae variable of ineres; in our case, he share of "wan a job" nonparicipans m = N w N w+n n. We can hen decompose he sock m ino he conribuion of he flows using a Taylor expansion of (10) around he mean of each hazard rae (λ AB λ AB Eλ AB ) m m = A B γ AB ( λ AB λ AB) + η (11) ). wih A, B {E, U, N w, N n } and { γ AB} he coeffi ciens of he Taylor expansion. Using (11) and daa on ransiion raes beween E, U, N w and N n over , 5 we can assess he separae conribuions of each hazard rae o movemens of m. 3 Some more facs This secion presens a number of addiional facs menioned in he main ex of he paper. 3.1 The behavioral differences beween N w and N n over ime To verify ha he informaion conveyed by he answer o he quesion "Wan a job" did no change oo much over ime, Figure 3 plos he evoluion of he relaive propensiies o join Unemploymen (U) and Employmen (E) for "Wan a job" (N w ) and "No wan a job" (N n ) nonparicipans: The solid line depics p N wu /p N nu and he dashed line depics p N we /p N ne. We can see ha he wo raios are remarkably sable over ime. 3.2 Srong wage growh over The second half of he 90s coincides wih srong posiive growh in real wages for all deciles of he income disribuion. Figure 4 shows he cumulaive changes in real wages since Recall ha ransiions in and ou of N w or N n are only available saring in

7 for differen perceniles of he wage disribuion. 6 Since higher wage leads o higher search inensiy of primary workers, srong wage growh is unlikely o explain he decline in desire o work hrough is effec on primary earners. However, large gains in wage income imply large gains in real family income, which can, hrough he added-worker effec, lead o lower desire o work among secondary workers. Figure 5 shows a sriking correlaion beween real median family income and he fracion of nonparicipans who do no wan a job. 4 A more general accouning framework: Allowing for separae ransiion raes for N w and N n labor force enrans The accouning framework underlying our resuls on he impac of a change in he share of "wan a job" nonparicipans on unemploymen and paricipaion were calculaed under he assumpion ha he ransiion of workers across labor marke saes could be described by a (four-sae) Markov chain of order 1, in ha only he curren labor marke sae is relevan o deermine an individual ransiion rae o anoher sae. This assumpion is sandard in he "Ins and Ous" lieraure ha uses a wo-sae (unemploymen and employmen) or a hree-sae (unemploymen, employmen, nonparicipaion) sock-flow accouning model o decompose unemploymen flucuaions ino he conribuions of is flows. 7 This assumpion amouns o summarizing worker heerogeneiy wih one variable: he curren labor marke saus. Naurally, his assumpion is a simplificaion of realiy as i is well known ha labor force enrans have differen unemploymen ouflow raes han job losers (e.g., Elsby e al., 2009) or ha long-erm unemployed have lower exi raes han shor-erm unemployed. In our paper, we made he same simplifying assumpion in a four-sae model of he labor marke, and we posied ha once a non-paricipan joins he labor force, he behaves like any oher unemployed or unemployed worker so ha his fuure ransiions do no depend on wheher ha individual was formally a "wan a job" or a "no wan a job" non-paricipan. In his secion, we es he sensiiviy of our resuls o ha approximaion by considering a richer framework in which we relax he assumpion ha a labor force enran ("wan a job" or no) behaves like he "average" labor force paricipan once he enered he labor force. Specifically, we posi ha labor force paricipans can be of wo ypes: (i) "New" labor force enrans and (ii) "Old" labor force enrans. Each ype is characerized by is own ransiion raes, and "New" enrans become "Old" a some consan Poisson rae υ. 8 6 A very similar picure holds for all he oher deciles of he income disribuion. Wage measures were consruced from he CPS Ougoing Roaion Group microdaa. 7 Fuja and Ramey (2009), Elsby e al. (2009), Shimer (2012), Elsby e al. (2013). 8 In fac, since a nonparicipan can be of wo ypes ("Wan a job" or "No wan a job"), we allow labor 7

8 4.1 Model Specifically, we consider a labor marke wih 8 saes: (E, U, N w, N n, U N w, E N w, U N n, E N n ). An Old labor force enran can be employed (E) or unemployed (U) and ransi beween hese saes or leave he labor force o become a "wan a job" nonparicipan (N w ) or a "no wan a job" nonparicipan (N n ). A "wan a job" nonparicipan (N w ) who joins he labor force is a New labor force enran, and he can be unemployed (U N w ) or employed (E N w ) and can hen ransi beween hese saes or leave he labor force. Similar noaions apply for a former "no wan a job" nonparicipan (U N n, E N n ). As saed previously, a New labor force enran becomes Old a a rae υ. Denoing Y = ( E, E N w, E N n, U, U N w, U N n, N w, N n) he vecor of he number of workers in each sae a dae, we have Y = P Y 1 (12) wih P a marix capuring ransiion probabiliies across saes during period. For insance, for E, we have E = (1 p EU p EN w p EN n )E 1 + U 1 p UE + E 1(1 N w e υ ) + E 1(1 N n e υ ) (13) wih (1 e υ ) capuring he probabiliy ha a "New" labor force enran becomes "Old" wihin one period. Similarly, for E N w, we have E N w = (1 p EN w U p EN w N w p EN w N n (1 e υ ))E N w 1 + N 1p w N w E N w (14) and similarly for E N n, U, U N w and U N n. Equaions (13) and (14) show how a labor force enran who is employed (E N w ) is allowed o have differen ransiion raes from an average employed worker (E). 4.2 Daa To measure he ransiion raes in and ou of E N w, U N w, E N n, U N n as well as measure υ, we mach he CPS micro daa over four consecuive monhly surveys, ha is we follow he labor force saus over four consecuive monhs. 9 force paricipans o be of hree ypes: (i) "new" labor force enrans from "Wan a job", (ii) "new" labor force enrans from "No wan a job" and (iii) "old" labor force enrans. 9 The CPS is a roaing panel where individuals are surveyed for four consecuive monhs, lef ou for eigh monhs, and hen surveyed again for four consecuive monhs. I is hus possible o follow an individual for four consecuive monhs. 8

9 To measure he ransiion raes in and ou of E N w, U N w, E N n, U N n, we proceed as in he 3- or 4-sae case. For insance, we compue he probabiliy p U Nw E by calculaing he probabiliy ha an individual who is an unemployed a and was a "wan a job" nonparicipan a 1 finds a job a ime + 1. We proceed similarly for he ransiion raes in and ou of E N n and U N n. To measure υ, he rae a which a New labor force enran becomes Old, we compare he average ransiion probabiliies of a labor force paricipan who enered he labor force 2 monhs ago wih he ransiion probabiliies of a labor force paricipan who enered he labor force one monh ago. Specifically, denoe p AB τ he measured ransiion probabiliy (beween sae A and B) of labor force enrans who enered he labor force τ imes ago. p AB 0 is hen he ransiion probabiliy of a labor force enran who jus enered he labor force. Denoe p AB he ransiion probabiliy of Old labor force enrans. Denoe N τ he number of New labor force enran who enered he labor force exacly τ imes ago. We have ha N τ evolves according o dn τ dτ = υn τ since New labor force enrans become Old a rae υ, which gives ha N τ N 0 = e υτ. We hen have ha he measured ransiion probabiliy of labor force enrans who enered τ periods ago is given by p AB τ = e υτ p AB 0 + (1 e υτ )p AB, (15) i.e., a weighed average beween he ransiion probabiliy of a New labor force enran and ha of an Old labor force enran, wih he weigh given by Nτ N 0, he fracion of labor force enrans who are sill New afer τ periods. Rewriing (15) a τ = 1 and τ = 2 and re-arranging, we ge ( p AB υ = ln 2 p AB p AB 1 p AB ). (16) Wih measures of p AB 2, p AB 1 and p AB we can hen recover υ hrough (16). To measure p AB 2 and p AB 1, we use he fac ha we can mach CPS micro daa over four consecuive monhly surveys. Firs, o measure p AB 1, he ransiion probabiliy of a labor force paricipan who enered he labor force one monh ago, we consider individuals who were 9

10 nonparicipans in monh 2, in he labor force in monh 3, and we calculae he ransiion probabiliies beween monh 3 and 4. Second, o measure p AB 2, he ransiion probabiliy of a labor force paricipan who enered he labor force 2 monhs ago, we consider individuals who were nonparicipans in monh 1, in he labor force in monh 2 and 3, and we calculae heir ransiion probabiliy beween monh 3 and 4. Measuring p AB is more diffi cul, since we canno follow a worker for more han 3 periods. Insead, we will approximae p AB wih p AB 3, he ransiion rae of individuals who enered he labor force more han 3 periods ago. To measure p AB 3, we consider individuals who were in he labor force in monhs 1 and 2, and we calculae heir ransiion probabiliy beween monh 3 and 4. Since υ can be calculaed from differen AB ransiions, we use he average value implied by (16) and obained for all possible AB ransiions wih A = {U, E} and B = {U, E, N w, N n }. We obain υ 0.2, which implies ha afer one quarer, 50 percen of a cohor of New labor force enrans have become Old. 4.3 Decomposiion of u and l Afer correcing for ime-aggregaion bias as in he four-sae case, we can use he sock-flow model (12) o quanify he conribuions of he rend in he N w -N n and N n -N w ransiion raes on he aggregae unemploymen rae. As shown in he main ex, hese wo ransiion raes accoun for mos of he flucuaions in he share of "wan a job" nonparicipans, and a variance decomposiion exercise using he generalized model (12) gives similar resuls wih a oal conribuion of abou 75 percen. From he seady-sae of (12), we can proceed as in he four-sae case and use a Taylor expansion around he mean of each hazard rae o decompose he variaions in unemploymen du due o he movemens in he flows λ N w N n and λ N n N w : du = φ N w N n ( λ N w N n λ N w N n ) + φ N n N w ( λ N n N w λ N n N w ). (17) We find ha he decline in m coming from movemens in λ N w N n and λ N n N w alone lowered unemploymen by abou.5 pp and labor force paricipaion by abou 1.9 pp. Thus, he resuls are similar (and confirm) he resuls repored in he paper using he simpler framework. Noe ha he resuls are acually sronger han in he main ex, because decomposiion (17) only capures movemens in λ N w N n and λ N n N w which accoun for "only" 75 percen of he decline in m. 10

11 5 A model of family labor supply We now presen a labor supply model wih inrafamilial choice. sylized and will focus only on individuals decision o ener he labor force. The model is deliberaely We consider a sequenial muliple-earner model in which he primary earner makes his/her work decision independenly of he secondary earners. The firs secondary earner, say he spouse, hen makes his/her labor supply decision by maximizing uiliy, aking accoun of he primary earner s income. The nex secondary earner, say a eenager living in he household, hen makes his/her labor supply decision in a similar fashion. And so on, for he oher family members. We posi ha here exis search fricions, so ha each worker mus search in order o ge a job, and a worker can increase his/her job finding probabiliy by increasing he inensiy of search. In he model, we inerpre he nonemploymen saes Nonparicipan who does no wan a job (N n ), Nonparicipan who wans a job (N w ) and Unemployed (U) as arbirary disincions inroduced by he household survey and is imperfec measuremen of search inensiy. Specifically, while search inensiy s is a coninuous variable, a survey canno precisely measure s. Insead, a household survey like he CPS can classify workers ino differen labor marke saes Nonparicipan who does no wan a job (N n ), Nonparicipan who wans a job (N w ) and Unemployed (U) ha correspond o differen inensiies of search. Specifically, wih s and s hreshold variables such ha 0 <s< s, an individual i is considered N n for s [0,s[, N w s [s, s[ and U for s [s, + [. We assume perfec consumpion pooling, so ha each household member has he same consumpion level and each family member aims o maximize aggregae consumpion ne of his/her disuiliy of searching for work. Finally, he family derives unearned income d ha is independen of labor marke saus, for insance asse income. The iming of he model is a follows: in he firs sage, he primary worker chooses search inensiy s, suffers a search disuiliy cos v(s) and finds a job wih probabiliy p(s). If unmached, he worker ges home producion income h. If mached, he job pays a salary w > h. In he second sage, he firs secondary worker solves a similar problem aking he income of he primary worker as given. As so on for he oher family members. Once each family member has made his/her labor supply decision, all workers ge paid, and he family consumes. In a family of size n, he problem of worker i {1, n} is hen max nu(c) v(s i) {c,s i } s.. nc = p(s i )(w i h i ) + d + h i + Ω i 1 11

12 where c is consumpion per capia, s i is search inensiy, and Ω i 1 = i 1 k=1 ω k is he oal income generaed by he "higher-order" workers wih ω k = {w k, h k } he income generaed by he k-h member. Ω i 1 is aken as given by he ih worker. For simpliciy, we specify sandard funcional forms for he funcions u(.), v(.) and p(.), and posi u(c) = ln(c), v(s) = χ 1+σ s s 1+σs and p(s) = p 0 s η, η < 1. I is easy o show ha s 1, he search inensiy of he primary worker, is deermined by he firs-order condiion χ 1 s σs 1 = np (s 1 )(w 1 h 1 ) p(s 1 )(w 1 h 1 ) + h 1 + d. (18) Proceeding similarly for he ih member of he family, s i is deermined by χ i s σs i = np (s i )(w h) p(s i )(w 1 h 1 ) + h + d + Ω i 1 (19) where he only difference is ha for secondary workers, he oal income generaed by he "higher-order" workers, Ω i 1, influences he search inensiy decision. From (18) and (19), one can isolae a number of model parameers ha influence search inensiy, and hus he fracion of nonparicipans who repor waning a job: 1. Heerogeneous or ime-varying preferences: Higher disuiliy of search lowers desire o s work: i χ < 0. i If he disuiliy of search varies wih demographic characerisics such as age, gender or educaion, search inensiy will vary wih demographic characerisics, and a change in he composiion of he populaion will affec he observed average desire o work. In addiion, a change in individual preferences could lead o a decline in desire o work. For insance, a larger decline in χ for children of working age would lead o a sronger decline in desire o work among his group. 2. Asse income: Higher asse income lowers search inensiy s i d < 0. A prominen example of a change in asse income is he large increase in neworh during he high-ech bubble of he lae 90s. 3. Reurns o employmen: (a) Higher wage increases desire o work among primary workers: s 1 w > 0. While higher wage increases he incenive o find a job (he subsiuion effec), i also raises expeced income which lowers he incenive o find a job (he income 12

13 effec). Overall, he ne effec is posiive. 10 Changes in he reurns o working can come from changes in marke wages or from changes in he ax code. (b) Higher wage has an ambiguous effec on desire o work among secondary workers: ds i dw = s i + s i dω i 1 }{{} w Ω }{{ i 1 }} dw {{} >0 <0 >0 0, i > 1. In addiion o he direc effec of higher reurns o employmen which increases search inensiy, higher employmen income lowers secondary workers search inensiy hrough he added-worker effec: As he family income generaed by "higherorder" workers increases hrough higher wages, desire o work amongs secondary workers decline ( s i Ω i 1 < 0). 4. Reurns o nonparicipaion: (a) Higher income from home producion lowers desire o work among primary workers: s 1 h < 0. (b) Higher income from home producion has an ambiguous effec on desire o work among secondary workers: ds i dw = s i + s i dω i 1 }{{} h Ω }{{ i 1 }} dh {{} >0 <0 0 0, i > 1. The ambiguiy occurs hrough he added-worker effec, as wih higher reurns o nonparicipaion, bu he mechanism is differen. Higher reurns o nonparicipaion has an ambiguous effec on family income ( dω i 1 dh 0), because while higher h raises Ω i 1 ceeris paribus, i also lowers he search inensiy oh higher-order workers, which lowers heir employmen rae and hus Ω i Naurally, his predicion sems from our choice of funcional forms for he uiliy funcion. We hink our model specificaion is reasonable, because is predicion is (i) in line wih sandard labor supply models, in which higher wages raise paricipaion, and (ii) consisen wih empirical evidence ha higher reurns o working increases paricipaion of unmarried individuals (e.g., Eissa and Leibman, 1996). 13

14 References [1] Abowd, J. and A. Zellner. "Esimaing Gross Labor-Force Flows," Journal of Business and Economic Saisics 3(3): , [2] Abraham, K. and R. Shimer. Changes in Unemploymen Duraion and Labor-Force Aachmen. in The Roaring Nineies, Russell Sage Foundaion, [3] Barnichon, R. and C. Nekarda. The Ins and Ous of Forecasing Unemploymen: Using Labor Force Flows o Forecas he Labor Marke, Brookings Papers on Economic Aciviy, Fall [4] Elsby, M. R. Michaels and G. Solon. The Ins and Ous of Cyclical Unemploymen, American Economic Journal: Macroeconomics, [5] Elsby, M. B. Hobijn and A. Sahin. On he Imporance of he Paricipaion Margin for Labor Marke Flucuaions, Working Paper, [6] Polivka, A. and S. Miller. The CPS Afer he Redesign: Refocusing he Economic Lens. in Labor Saisics and Measuremen Issues, edied by John Haliwanger, Marilyn Manser, and Rober Topel. Universiy of Chicago Press, 1998 [7] Poerba, J. and L. Summers Reporing Errors and Labor Marke Dynamics, Economerica, Economeric Sociey, vol. 54(6), pages , November [8] Shimer, R. "Reassessing he Ins and Ous of Unemploymen," Review of Economic Dynamics, vol. 15(2), pages , April,

15 pp of LFPR pp of Ur U ss Approximaion Figure 1: Seady-sae unemploymen rae ("U ss ") and unemploymen prediced by our accouning decomposiion ("Approximaion"), LFPR ss Approximaion Figure 2: Seady-sae labor force paricipaion rae ("LFPR ss ") and paricipaion rae prediced by our accouning decomposiion ("Approximaion"),

16 Log poins Relaive propensiy o join U Relaive propensiy o join E Figure 3: Relaive propensiies o join Unemploymen (U) and Employmen (E) for "Wan a job" (N w ) and "No wan a job" (N n ) nonparicipans. The solid line depics p N wu /p N n U and he dashed line depics p N we /p N ne. 4-quarer moving averages,

17 Cumulaive percen change since h 40h 80h Figure 4: Cumulaive change in real hourly wages of all workers, by wage percenile,

18 Median real household income per household (righ scale) Fracion of "No wan a job" (lef scale) 68, , ,000 56, , Figure 5: Median real income per household (in housands of 2010 US$, righ scale) and fracion of nonparicipans who repor "No waning a job" (lef scale),

19 Cange in wan job probabiliy Change in wan job probabiliy Change in wan job probabiliy Cange in wan job probabiliy Change in wan job probabiliy Panel A. By Age (relaive o 16 19) Age Panel B. By Educaion (relaive o no HS Deg) Panel C. By Gender (relaive o Female) No HS Deg HS/Some Coll Coll Grad Educaion Female Gender Male Panel D. By school saus (relaive o no in school) Panel E. By Posiion in Household (rel. o head) No in school School saus In school Head Spouse Child Oher Posiion in Household Figure 6: Demographic deerminans of desire for work. Coeffi cien esimaes of regression of "desire for work" on individual characerisics, The black bars denoe he poin esimaes and he red bars denoe ±2 sandard-errors. 19

20 UE ransiion probabiliy Figure 7: Monhly ransiion probabiliy from Unemploymen o Employmen, quarer moving average. 20

21 Hazard rae Hazard rae N w >U N n >U N w >E N n >E Figure 8: Monhly ransiion rae from "Wan a job" (N w ) o Unemploymen (U) (op-lef panel), from "No wan a job" N n o U (op-righ panel), from N w o Employmen (E) (boom-lef panel), and from N n o E (boom righ panel). 4-quarer moving average,

22 Transiion probabiliy Transiion probabiliy N n > N w N w > N n Figure 9: Monhly ransiion probabiliy from "No wan a job" (N n ) o "Wan a job" (N w ) (op panel) and from "Wan a job" (N w ) o "No wan a job" (N n ) (boom panel). 4-quarer moving average,