Unemployment in the Stock and Flow

Unemployment n the Stock and Flow by Mchael Baker*, Mles Corak** and Andrew Hesz*** No. 97 11F0019MPE No. 97 ISSN:1200-5223 ISBN: 0-0660-16579-1 Prce: $5.00 per ssue, $25.00 annually Busness and Labour Market Analyss, Statstcs Canada 24 R.H. Coats Buldng, Ottawa, K1A 0T6 *Unversty of Toronto **Statstcs Canada (613) 951-9047 ***Statstcs Canada (613) 951-3748 Facsmle Number: (613) 951-5403 September 1996 Helpful dscussons wth Davd Burne, Steve Jones, Georges Lemaître, Alce Nakamura, Thomas Nardone, and Deborah Sunter are acknowledged wth thanks, as are the comments of semnar partcpants n the Analytcal Studes Branch of Statstcs Canada, the Research Department of the Bank of Canada, and the CSLS-CERF preconference on the Canada-U.S. unemployment rate gap. A prevous verson of ths paper was presented to the 1995 meetngs of the Canadan Economcs Assocaton held at the Unversté du Québec à Montréal, to the 1996 meetngs of the Alled Socal Scences Assocaton, and to the CSLS-CERF conference held n Ottawa, February 1996. The authors may be reached at baker@epas.utoronto.ca or at coraml@statcan.ca. Ths paper represents the vews of the author(s) and does not necessarly reflect the opnons of Statstcs Canada. Auss dsponble en franças

Table of Contents Table of Contents Abstract v 1. Introducton 1 2. Methodology 2 3. Results for Canada 4 4. A Canada - U.S. Comparson 9 5. Implcatons for Explanatons of the Canada-U.S. Unemployment Rate Gap 17 6. Concluson 20 Data Appendx 21 Bblography 22 Analytcal Studes Branch - Research Paper Seres - - Statstcs Canada No. 11F0019MPE No. 97

Abstract A framework for the dynamc analyss of unemployment s presented, and appled to Canadan and U.S. data. The focus of the analyss s upon the dstncton between beng unemployed and becomng unemployed, that s, between the stock and the flow of unemployment. The share of a partcular group n the stock of unemployed wll dffer from ts share n the flow nto unemployment to the extent that the average duraton of unemployment for the group dffers from the economy wde average. An analyss of Canadan and U.S. data leads to a seres of stylzed facts that permt a deeper understandng of unemployment n the two countres, and of the dfferences between them. Sgnfcant dfferences n the average duraton of unemployment mply that stock shares are not good ndcators of flow shares, changes n the stock share of some groups are due to changes n the flow share, whle for others they are due to changes n the length of unemployment spells. Explanatons of the Canada - U.S. unemployment rate gap should try to accommodate at least three facts uncovered by the analyss: (1) that employer ntated permanent separatons are the prmary means of entry nto unemployment n Canada, whle labour force entry plays a more mportant role n the US; (2) unemployment spells are sgnfcantly longer n Canada than n the U.S. because of longer spells for most groups regardless of reason for unemployment, not because of a compostonal dfference n the make up of the unemployed; and (3) that longer spell duraton and a hgher ncdence of unemployment contrbute about equally to the trend ncrease n the Canada - U.S. unemployment dfferental durng the 1980s. Keywords: Unemployment, Duraton, Incdence Analytcal Studes Branch - Research Paper Seres - v - Statstcs Canada No. 11F0019MPE No. 97

1. Introducton It has long been recognzed that labour markets are very dynamc markets, and more partcularly that unemployment s a state through whch many people pass. Feldsten's characterzaton of the new unemployment durng the early 1970s as well as subsequent work by Clark and Summers ushered n ths awareness for many observers. Further, many theoretcal explanatons of the level and changes n unemployment, as well as the ratonale for polcy nterventon rests on the dstncton between the ncdence and duraton of unemployment spells. To understand unemployment t s mportant to apprecate the dstncton between beng unemployed, and becomng unemployed, that s between the stock of unemployed and the flow nto unemployment. In ths study we present a framework for the analyss of unemployment stocks and flows, and apply t to the level of unemployment n Canada, to changes n t, and to a comparson between Canadan and U.S. data. At the core of our analyss s the relatonshp between the share of a partcular group n the stock of unemployed and ts share n the flow of those becomng unemployed. The extent to whch these shares dffer depends upon the average length of unemployment spells relatve to the economy wde average. Those groups spendng a relatvely longer tme unemployed wll form a greater proporton of the stock of unemployed than they wll of the flow. Lkewse those experencng relatvely shorter spells of unemployment wll form a greater proporton of the flow nto unemployment than they wll of the stock. We examne data from the Canadan Labour Force Survey (LFS) over the perod 1977 to 1995 stratfed by gender and reason for unemployment. The latter ncludes ob loss (ether a temporary or a permanent layoff), quts, and entry or re-entry nto the labour market. We fnd sgnfcant dfferences n the average duraton of unemployment spells across these groups that lead to correspondng dfferences n ther stock and flow shares. For example, the stock share of temporary layoffs s typcally one half to one thrd ther entrance share because the average duraton of an unemployment spell for those temporarly lad-off s about one half the economy wde average. Also, among men, the stock share of ob losers s roughly 30% hgher than the flow share. We also examne varatons n these shares, and fnd frst, that the share of unemployment due to temporary ob loss falls durng a recesson. Ths s not as a result of any changes n the share of nflows, but rather because those temporarly lad off do not experence any change n the average duraton of unemployment spells even though the economy-wde average duraton ncreases sgnfcantly. Second, among men, the ncrease n the stock share of ob losers n a downturn overstates ther mportance as a source of spells. Fnally, for women, labour market re-entry s a more mportant source of unemployment spells durng these perods than varaton n ts stock share suggests. Our comparatve analyss of Canadan and U.S. data covers the perod 1980-1988. We fnd that temporary layoffs are a more mportant source of unemployment spells n the U.S., whle permanent ob loss s more mportant n Canada. Whle there s some queston as to whether these concepts are comparable between the LFS and the Current Populaton Survey (CPS), t remans true that employer ntated separatons are the source of over 50% of unemployment nflows n Canada versus closer to 40% n the U.S. Analytcal Studes Branch - Research Paper Seres - 1 - Statstcs Canada No. 11F0019MPE No. 97

Fnally, we also examne how the level of, and varaton n, the Canada - U.S. unemployment rate dfferental s related to dfferences n unemployment duraton and ncdence over ths perod. We fnd that the cyclcal ncrease n the unemployment rate gap durng the recesson of the early 1980s was prmarly the result of much longer unemployment spells n Canada. However, the trend ncrease n the unemployment rate over the perod s accounted for almost equally by the effects of ncdence and duraton. We also note that the duraton dfferental s the result of dfferences n average duraton wthn groups, rather than dfferences n the composton of the unemployed between the two countres. We present these fndngs as a set of stylzed facts that explanatons of the Canada - U.S. unemployment rate gap must be able to accommodate, and go on to draw some possble nferences. Canada - U.S. dfferences n average duraton by reason for unemployment suggest that Canada s relatvely more generous UI program may play some part n the dfferental. On the other hand, the average spell duratons of labour market new entrants and re-entrants are also longer n Canada than n the U.S., and these groups are less lkely to be covered by UI n both countres. Ths result suggests there may be other forces at work. Our evdence also suggests that the employer ntated ext rate from employment nto unemployment s hgher n Canada. Whle ths result s consstent wth recent evdence that the Canadan UI system may nduce churnng n the labour market, we are unable to dentfy a defntve role to ths program n our data. Future research on dfferences n the ncdence of unemployment across the two countres may shed further lght on ths ssue. 2. Methodology Our analytcal framework draws on the research of Chesher and Lancaster (1981, 1983) and Salant (1977). The key dstncton s between what we refer to as the entrance share and stock share of a group of unemployed ndvduals. We dvde the unemployed nto mutually exclusve and collectvely exhaustve groups. The entrance share of a partcular group s defned as the fracton of the total number of ndvduals becomng unemployed accounted for by members of that group. For example, f the groups are ndexed by, let N (x,t) represent the number of ndvduals belongng to that group who have been unemployed for x months at tme t. Further, let the absence of a subscrpt ndcate an economy wde total. Then the entrance share of group at tme t s (1) s () t = N( 0, t). N( 0, t) The stock share of group s defned as the share of the total number of unemployed at tme t accounted for by members of the group. In ths case, let U (t) denote the number of ndvduals wth group characterstcs unemployed at tme t. The stock share s gven as: (2) U () t Ut () N (,) 0t D () t N(,) 0t D() t σ =. The second part of ths expresson reles upon the famlar steady state dentty that the number of unemployed s equal to the product of the number of ndvduals becomng unemployed and the average completed duraton of an unemployment spell, whch s denoted as D(t). Analytcal Studes Branch - Research Paper Seres - 2 - Statstcs Canada No. 11F0019MPE No. 97

The relatonshp between the stock share and the entrance share s derved by combnng equatons (1) and (2): (3) σ = () Dt (). s D t Ths equaton shows that the stock share s the entrance share weghted by the relatve average spell duraton. If the members of group experence unemployment spells that are on average the same length as the average economy wde spell then the stock share of that group wll be the same as ts entrance share. Otherwse t wll dffer, beng larger for those groups wth longer spell lengths, and lower for those wth shorter spells. Gven an estmate of ether the stock share or the entrance share the other can be derved f nformaton on the average duraton of unemployment for the group and the economy as a whole are also avalable. The average complete duraton of unemployment can be calculated from nformaton on reported spell lengths. The rato S(x,t)=N(x,t)/N(x-1,t-1), whch we call the contnuaton rate, offers an estmate of the condtonal probablty that an ndvdual wll stay unemployed at least to the xth month gven that he or she has been unemployed x-1 months. In other words, ths probablty can be estmated as the rato of the number of ndvduals reportng to be unemployed x months at tme t dvded by the number reportng to be unemployed x-1 months at tme t-1. These contnuaton rates are used to calculate the average complete duraton of unemployment as: (4) n Dt () = S( t,) x= 1 x = 1. Ths s the dscrete tme verson of the result that n contnuous tme the average duraton of unemployment s the ntegral of the survvor functon. 1 Equaton (3) refers to the level of stocks and flows, but an analogous relatonshp between changes n them can be derved by takng the natural logarthm of (3) and dfferentatng wth respect to a cyclcal ndcator. Referrng to ths ndcator as C, and expressng the results as elastctes yelds: (5) ε = ε + [ ε ε ]. σ C s C DC DC In other words, the percentage change n the stock share s the result of two factors: how much the entrance share changes, and how much spell duraton changes relatve to the economy wde change n average spell duraton. By approachng the problem n ths way we are not suggestng that the labour market s actually n a steady state throughout the process of change. Rather, we are nvokng a thought experment nvolvng a comparson of two steady states: one n whch the economy s held n a 1 See Baker (1992a), Baker and Trved (1985), and Sder (1985) for more detals. Analytcal Studes Branch - Research Paper Seres - 3 - Statstcs Canada No. 11F0019MPE No. 97

steady state wth the confguraton of nflow and contnuaton rates that characterze the cyclcal peak, and the other n whch these rates are those of the cyclcal trough. 2 3. Results for Canada Canadan data on stocks, flows, and the duraton of unemployment are used for the perod from January 1977 through September 1995. To be consdered as unemployed respondents to the LFS must be wthout pad employment durng the reference week, and (unless they are temporarly lad-off and expect to be recalled) lookng for work. If the ob search requrement s not met the ndvdual s classfed as not n the labour force. Indvduals who are searchng for ther frst ob are classfed as new entrants, whle those who have re-entered the labour force after a perod out of t are classfed as re-entrants. Those who are not temporarly lad-off, have held employment n the past, and have not left the labour force snce ther last ob separaton are asked f they qut ther last ob. Thus the unemployed are classfed nto one of the followng groups: temporarly lad-off, other ob losers (essentally those permanently lad off), qutters, new entrants, or re-entrants. 3 The stock shares of unemployed are based on counts of the number of unemployed, approprately weghted to represent country wde totals. The entrance shares are derved from the subset of ndvduals reportng less than fve weeks of unemployment, that s those who would not have been unemployed durng the prevous month's survey. 4 The reported duraton of unemployment s the number of weeks of contnuous ob search up to and ncludng the reference week of the survey. Ths s used to derve estmates of the average complete duraton, usng equaton (4), the detals beng descrbed n Corak (1993). 5 The data assocated wth equaton (3), stock and entrance shares as well as group specfc and the economy wde average duraton of unemployment, are presented n Table 1. The stock of unemployed s domnated by those who have permanently lost ther obs. Ther stock share s 49%. Males who experenced permanent layoffs are the most numerous, comprsng 33% of the stock of unemployed. Female permanent ob losers consttute the second largest group wth a stock share of 16%. However, women who have re-entered the labour market also represent a sgnfcant fracton (14%) of the total stock share. The smallest stock shares are accounted for by new entrants and those temporarly lad-off. Together these groups make up about 10% of the unemployed. 2 3 4 5 In other words we are answerng the followng queston: If the economy were n a steady state defned by the nflow and ext rates that prevaled at the cyclcal peak and then n another steady state defned by the rates that prevaled at the cyclcal trough, what are the dfferences n the stock shares, and are they the result of dfferences n entrance shares or n relatve spell duraton? The other ob losers category ncludes, n addton to those permanently lad-off, those whose contracts expred and those who were fred. In what follows we refer to ths category smply as the permanently lad-off. Statstcs Canada (1992) offers more detal on the methodology of the LFS. Some ndvduals may have become unemployed and ether found a ob or left the labour force after a very bref spell of unemployment durng the month between consecutve surveys. As a result changes n entrance shares may be due n part to relatve changes n the average duraton of unemployment spells of less than one month n length. In addton, some mnor adustments to these numbers s made to account for a reportng bas nherent n the data. In actual fact monthly transton probabltes are derved for the frst three months of unemployment. Mult-month perods are used at longer duratons because of sample sze lmtatons. Ths s essentally the same method used by Baker (1992a). Analytcal Studes Branch - Research Paper Seres - 4 - Statstcs Canada No. 11F0019MPE No. 97

A comparson of stock shares and entrance shares llustrates that nether statstc should be assumed to be a good ndcator of the other. Permanently lad-off men have the largest entrance share, but at 26% t s 7 percentage ponts less than ther stock share. For women permanent layoffs may be the largest reason for beng unemployed, but labour force re-entry s the most sgnfcant reason for becomng unemployed. The entrance share of permanently lad off women s 14%, 2 percentage ponts less than ther stock share. Female re-entrants, on the other hand, have an entrance share of 17%, 3 percentage ponts hgher than ther stock share. For both genders the entrance shares for temporary layoffs are more than double the stock shares, suggestng that they are a much more mportant source of unemployment spells than they are of unemployment. The dfferences between entrance and stock shares are explaned by the dfferences between the group specfc and economy wde average duraton of unemployment. The average duraton of unemployment for men who have been permanently lad-off s more than 4 weeks longer than the economy wde average. As a result stock shares exceed entrance shares for ths group by a sgnfcant margn. In contrast, female re-entrants experence unemployment spells that are about three weeks shorter than the economy wde average wth the result that the stock share of ths group s lower than ts entrance share. In a smlar fashon, the stock shares of those temporarly lad off are less than half of the entrance share because the duraton of unemployment for these groups s so much shorter than the economy average. Analytcal Studes Branch - Research Paper Seres - 5 - Statstcs Canada No. 11F0019MPE No. 97

Table 1 Stock Shares, Entrance Shares, and the Average Duraton of Unemployment: Canada, 1977:01-1995:09 Stock Share (σ ) Entrance Share (s ) Average Duraton (D ) weeks Economy Wde 16.5 Men Temporary Layoffs 0.04 0.09 9.0 Permanent Layoffs 0.33 0.26 20.7 Quts 0.09 0.07 21.3 New Entrants 0.02 0.02 20.0 Re-Entrants 0.10 0.11 15.2 Women Temporary Layoffs 0.02 0.06 7.2 Permanent Layoffs 0.16 0.14 19.8 Quts 0.08 0.06 20.8 New Entrants 0.02 0.03 16.7 Re-Entrants 0.14 0.17 13.7 Analytcal Studes Branch - Research Paper Seres - 6 - Statstcs Canada No. 11F0019MPE No. 97

Table 2 Elastctes of Stock Shares, Entrance Shares, and Average Duraton of Unemployment wth Respect to the Unemployment Rate: Canada, 1977:01-1995:09 Elastcty of Entrance Share Elastcty of Average Duraton Economy Wde 0.660 (0.030) Predcted Stock Share Elastcty Men Temporary Layoffs 0.173 (0.098) Permanent Layoffs 0.465 (0.033) Quts -1.099 (0.059) New Entrants 0.401 (0.122) Re-Entrants -0.089 (0.051) Women Temporary Layoffs -0.143 (0.080) Permanent Layoffs 0.377 (0.047) Quts -0.865 (0.073) New Entrants 0.059 (0.111) Re-Entrants -0.278 (0.036) ( ) Indcates standard error. * Indcates a sgnfcant dfference from the economy wde elastcty. 0.055* (0.118) 0.769* (0.053) 0.981* (0.094) 0.844 (0.209) 0.714 (0.089) 0.091* (0.074) 0.583 (0.065) 0.652 (0.104) 0.746 (0.155) 0.483* (0.061) -0.432 (0.091) 0.574 (0.052) -0.778 (0.112) 0.585 (0.234) -0.035 (0.092) -0.712 (0.106) 0.300 (0.070) -0.873 (0.129) 0.145 (0.199) -0.455 (0.065) Analytcal Studes Branch - Research Paper Seres - 7 - Statstcs Canada No. 11F0019MPE No. 97

The cyclcal elastctes of the entrance shares, group specfc duraton, and economy wde duraton of unemployment are derved by regressng the natural logarthms of group specfc shares (s (t)), group specfc duraton (D (t)), and aggregate duraton (D(t)) respectvely upon the natural logarthm of the unemployment rate, monthly dummy varables to control for seasonal effects, and a tme trend. These estmates are then used n conuncton wth equaton (5) to construct the predcted stock share elastctes. The results are presented n Table 2. Entrance share elastctes are postve for those (of ether gender) permanently lad-off, for temporarly lad-off males, and male new entrants. They are negatve for qutters of both genders, and females who are re-entrants or have been temporarly lad-off. The shares of qutters are the most cyclcally senstve (the elastcty for men beng almost -1.1, whle that for women beng -0.9), followed by those of the permanently lad-off and male new entrants (whch range from 0.38 to about 0.47). Thus, a steady state ncrease of the unemployment rate mples a declne n the share of qutters and female labour force re-entrants, and a rse n the share of those permanently lad-off and males seekng ther frst ob. As equaton (5) makes clear the nfluence of these changes on changes n stock shares s medated by the average duraton of unemployment: stock share elastctes wll dffer from entrance share elastctes to the extent that the dfference between the elastctes of group specfc and economy wde average duraton s sgnfcantly dfferent from zero. Ths turns out to be so n fve cases: for males who are temporarly lad-off, permanently lad-off, or qut; for females who are temporarly lad-off, and who are labour force re-entrants. 6 In all the other cases, varatons n stock shares are essentally the result of changes n entrance shares. In fact, the proporton of stock share varaton due to entrance share varaton may be consdered to be εsc equal to. 7 In two of the fve cases for whch dfferences n the elastctes of average duraton matter n determnng stock share varatons the entrance share s stll domnant, εsc + εdc εdc accountng for 81% of the change n the stock share of permanently lad-off males, and 77% of the change n the stock share of males who have qut. For the former group varatons n duraton strengthen the effect of changes n entrance shares, whle for the latter they attenuate t. In the reman- 6 Ths s determned by regressons of the dfference between the logarthms of the group specfc and the economy wde spell duraton aganst the logarthm of the unemployment rate, monthly dummes, and a tme trend. The unemployment coeffcent estmates (followed by standard errors) are: Temporary Layoffs Permanent Layoffs Quts New Entrants Re-Entrants Males -0.605 (0.115) 0.109 (0.042) 0.320 (0.092) 0.184 (0.203) 0.054 (0.078) Females -0.569 (0.076) -0.077 (0.056) -0.008 (0.101) 0.085 (0.150) -0.177 (0.055) Those coeffcents wth a t-statstc ò 1.9 are consdered statstcally sgnfcant n Table 2. 7 It should be noted, however, that εdc ε DC s also affected by varatons n entrance shares through ther nfluence on the economy wde average duraton of unemployment. The average complete duraton of unemployment may be expressed as a weghted average of the group specfc duratons, D() t = s() t D() t. Thus changes n entrance shares have a drect and ndrect channel to nfluence stock shares. To estmate the amount of stock share varaton whch s mpled by entrance share varaton we need to account for the drect effect of ε sc as well as the ndrect effect through varaton n ε DC. To measure the varaton n the economy wde duraton due the change n entrance shares we calculate D*( t) = s( t) D where D s the group specfc average duraton for the entre perod. That s, we hold group specfc duraton constant and let the entrance shares take ther actual values so that any varaton n the aggregate duraton s due solely to the latter. A regresson of D * (t) on the explanatory varables used n the text reveals an elastcty of D * (t) wth respect to the unemployment rate of only 0.010 wth a standard error of 0.008. On ths bass we conclude that the varaton n aggregate duraton due to varaton n entrance shares s neglgble. Analytcal Studes Branch - Research Paper Seres - 8 - Statstcs Canada No. 11F0019MPE No. 97

ng three cases dfferences n duraton are an mportant f not domnant nfluence, accountng for most of the mpact on stock varaton for those temporarly lad-off (about 80%), and a substantal fracton (40%) n the case of female re-entrants. In summary, changes n stock shares reflect, for the most part, changes n entrance shares. In some cases, however, changes n entrance shares are ether a neglgble nfluence on stock shares, or ther nfluence s medated through changes n relatve spell duraton. A steady state ncrease n the unemployment rate wll, for example, mply a fall n the stock share of those temporarly lad off not because they form a smaller proporton of the nflow nto unemployment, but because these ndvduals experence a neglgble change n the average length of tme they wll be unemployed. 4. A Canada - U.S. Comparson After followng one another qute closely for most of the post-war perod, a marked gap has arsen between the Canadan and U.S. unemployment rates. Between 1982 and 1994 the U.S. unemployment rate averaged 7%, but the Canadan rate averaged 10%. In spte of beng the subect of numerous studes ths gap remans to be satsfactorly explaned. 8 The focus of ths lterature has been on the unemployment rate: there have been no comparatve analyses of the ncdence or duraton of unemployment. 9 Wth ths n mnd a comparson usng our framework may be nformatve. The U.S. data needed to calculate the average complete duraton of unemployment are avalable to us only from 1980 to 1988. 10 Consequently, our results offer a characterzaton of the unemployment rate gap durng the 1980s. Card and Rddell (1995) have ponted out that ths perod should be dstngushed from the 1990s. 11 In short, we are not n a poston to make a comparson between pre- and post-gaps perods, only an assessment of the nature of unemployment n the two countres durng the latter, and wth the caveat that our analyss may not apply to developments snce the onset of the 1990s. Three dfferences are mmedately apparent between the two countres when the data are presented usng the relatonshp descrbed n equaton (3), (see Table 3). Frst, for all groups except temporary layoffs, the average length of a completed spell of unemployment s much longer n Canada than n the U.S. The dfference s almost fve weeks n the aggregate, but can be as long as 9.4 weeks for those who have qut. Second, the stock and entrance shares of the temporarly lad-off are hgher n the U.S. than n Canada, the former partcularly so. In the U.S., 18% of unemployment spells and 16% of unemployment are assocated wth temporary layoffs, compared to 14% and 6% n Canada. The flpsde of ths s that unemployment spells caused by permanent ob loss, whch are longer on average n both 8 9 10 11 See Ashenfelter and Card (1986), Card and Rddell (1993, 1995), Corak and Jones (1995), Dumas (1984), Fortn (1994), McCallum (1987, 1988), Mlbourne, Purvs and Scoones (1991), Sebert and Zad (1994), Storer (1993), Zagorsky (1993, 1994). Crémeux and Van Audenrode (1995), and Tlle (1995) are recent exceptons. Further, the US nformaton s lmted only to the out gong rotaton groups of the CPS. Ths restrcts the sample sze, and prevents us from performng the analyss by gender. The unemployment rate gap durng the 1990s s characterzed by a sharp ncrease n non-employment rates n Canada relatve to the US, and by a sharp decrease n partcpaton rates. Durng the 1980s both these rates were slghtly hgher n Canada. Analytcal Studes Branch - Research Paper Seres - 9 - Statstcs Canada No. 11F0019MPE No. 97

countres, are relatvely more prevalent n Canada. Both the entrance and stock shares of permanent layoffs are 12 to 14 percentage ponts hgher n Canada than n the U.S. The thrd maor dfference concerns new entrants, a group that forms a much larger share of U.S. unemployment than t does of Canadan. At 14% the entrance share of new entrants s almost three tmes as great n the U.S., whle ther stock share (at 11%) s more than double the Canadan fgure. These fndngs rase at least two ssues concernng methodologcal dfferences between the LFS and the CPS. The frst deals wth the manner n whch nformaton on the temporarly lad-off s captured. It has long been suspected that the CPS overestmates the numbers nvolved, whle the LFS underestmates them. The U.S. questonnare refers to the state of beng temporarly lad-off as smply beng on layoff. Over tme the popular usage of the term layoff has changed wth the result that more and more respondents may have taken t to mean permanent layoff. It has been suggested that the number temporarly lad-off has been overestmated by 30% to 50%. In fact, the ntroducton of a revsed questonnare n 1994 (whch addresses ths problem wth a new seres of questons) dd not lead to sgnfcant changes n the number of temporarly lad off or to the composton of the unemployed. 12 The LFS, n contrast, s thought to underestmate the number of ndvduals lad off and expectng to be recalled. Ths bas could be n the order of 25%, rasng the entrance share to about 17% or 18% and the stock share slghtly to 7% or 8%. 13 All of ths s to suggest that the dfferences between the entrance shares of the temporarly lad-off s lkely even less than that depcted n Table 3. Indeed, the fgure may even be slghtly hgher n Canada than n the U.S. At the same tme, however, the U.S. stock share probably remans sgnfcantly hgher than the Canadan. 14 The second methodologcal ssue concerns the defnton of a new entrant. In the CPS those who have never held a full-tme ob longer than two consecutve weeks are consdered to be new entrants, whle n the LFS only those who have never held a ob - of any sort - fall nto ths category. Table 3 Stock Shares, Entrance Shares, and the Average Duraton of Unemployment: Canada and Unted States, 1980-88 12 13 14 See Bregger and Dppo (1993), and Polvka and Rothgeb (1993) for a dscusson of the ssue. We thank Thomas Nardone of the BLS for pontng out that the questonnare revsons dd not lead to sgnfcant changes n the composton of the unemployed, even though the qualty of the estmate may have been mproved. Cohany, Polvka, and Rothgreb (1994) document ths fact. Ths expectaton s based upon the results of a small plot study conducted by Statstcs Canada, the results of whch have not been publshed. The bas orgnates wth Queston 30 of the LFS, whch drects ntervewers to a seres of questons that determne f the respondent s temporarly lad-off. The wordng of the queston s thought to screen out many respondents who n fact have a recall expectaton. It should also be noted that the LFS appled a search test to those who have been temporarly lad off longer than sx months for part of our sample perod. An ndvdual who has been lad off longer than sx months, and who has not reported actvely searchng for work n the four weeks before the survey s re-classfed as out of the labour force. Ths edt, however, has not been appled after 1982, and we therefore expect that t does not play a role n determnng our fndngs. We thank Deborah Sunter and Ian Macrede of Statstcs Canada for brngng these ssues to our attenton. It should also be noted that recall expectatons may vary over the course of an unemployment spell. For example, usng admnstratve data on Canadan UI clamants, Corak and Pyper (1995, table 4-1) note that 77% to 87% of clamants are told by ther employers at the tme of layoff that they wll be recalled, but ultmately only about 55% end up beng recalled. In ther analyss of UI clamants n two US states, Katz and Meyer (1990) fnd errors n recall expectatons of a roughly smlar magntude: 20% to 30% of those expectng recall at the tme of layoff were not recalled. It s possble that unaccounted dfferences n the way the two labour force surveys ncorporate recall expectatons, and dfferences n edtng procedures that are mplctly or explctly based on a lkelhood of recall over the course of an unemployment spell (as dscussed n the prevous note) may nfluence our results. Analytcal Studes Branch - Research Paper Seres - 10 - Statstcs Canada No. 11F0019MPE No. 97

Stock Share Entrance Share Average Duraton (weeks) Canada U.S. Canada U.S. Canada U.S. Economy Wde 16.3 11.6 Temporary Layoffs 0.06 0.16 0.14 0.18 7.4 11.7 Permanent Layoffs 0.48 0.36 0.39 0.25 20.1 17.3 Quts 0.17 0.12 0.14 0.13 20.6 11.2 New Entrants 0.05 0.11 0.05 0.14 15.7 10.8 Re Entrants 0.24 0.25 0.28 0.30 13.8 9.5 Table 4 Elastctes of Stock Shares, Entrance Shares, and Average Duraton of Unemployment wth Respect to the Unemployment Rate: Canada and Unted States, 1980-88 Elastcty of Entrance Share Elastcty of Average Duraton Predcted Stock Share Elastcty Canada U.S. Canada U.S. Canada U.S. Economy Wde 0.664 (0.037) Temporary layoffs 0.002 0.296 0.032* (0.104) (0.097) (0.066) Permanent Layoffs 0.494 0.399 0.695 (0.032) (0.062) (0.053) Quts -0.959-1.207 0.832* (0.061) (0.092) (0.079) New Entrants 0.020 0.116 0.764 (0.095) (0.090) (0.156) Re Entrants -0.218-0.130 0.566* (0.039) (0.053) (0.073) ( ) Indcates standard error. * Indcates a sgnfcant dfference from the economy wde elastcty. 0.619 (0.065) 0.212 (0.224) 0.719 (0.156) 0.544 (0.193) 0.516 (0.223) 0.397* (0.095) -0.629 (0.109) 0.525 (0.045) -0.792 (0.088) 0.120 (0.178) -0.316 (0.067) -0.111 (0.234) 0.449 (0.135) -1.282 (0.205) 0.013 (0.229) -0.352 (0.107) Analytcal Studes Branch - Research Paper Seres - 11 - Statstcs Canada No. 11F0019MPE No. 97

Very roughly, the number of new entrants n Canada s about the sze of a one-year age cohort; n the U.S. t would be sgnfcantly greater. Ths s the lkely explanaton for the substantal dfferences n both the entrance and stock shares of new entrants presented n Table 3. 15 Takng both of these factors nto account t s stll approprate to suggest that ob separaton s a more mportant source of unemployment n Canada than n the U.S., whle labour market entry (broadly defned to nclude new entrants and re-entrants) s more mportant n the U.S. In spte of some queston as to the dvson of the unemployed between temporary and permanent lay-offs, the latter s lkely a more mportant component of the entrance share n Canada, beng at least 10 percentage ponts hgher than n the U.S. On the other hand, labour force entry and re-entry together account for 33% of the entrance share n Canada, but 44% n the U.S. All of ths also holds for the stock shares. A comparson of cyclcal varaton n the stock and flow shares s presented n Table 4. The most notable dfference n the entrance share elastctes s that the entrance share of temporary layoffs ncreases wth an ncrease n the unemployment rate n the U.S., but remans unchanged n Canada. For the other groups there are dfferences n magntude, but the pattern s very smlar. The elastcty of aggregate duraton s very smlar n these countres over ths perod. 16 There are, however, some dfferences at the group level. For example, the elastcty of the average duraton of qutters s larger n Canada than n the U.S. On the other hand, the elastctes for ob losers are roughly smlar, and the spells of the temporarly lad off appear acyclcal n both countres. At the same tme, however, the duraton of unemployment for those temporarly lad-off changes sgnfcantly less than the economy wde average duraton n Canada. 17 Consequently, the results for the predcted stock share elastctes reveal that the share of temporary layoffs falls as the unemployment rate rses n Canada, but dsplays lttle movement n the U.S. Also, the elastcty for quts s larger n the U.S. than n Canada. In summary, over the sample perod employer ntated separatons are a relatvely larger source of unemployment spells n Canada, whle n the U.S. labour market entry plays the larger role. Further, varatons n entrance shares are roughly smlar n the two countres, except for the fact that the share of temporary layoffs ncrease wth ncreases n the unemployment rate n the U.S., but does not change n Canada. Fnally, unemployment spells appear to be sgnfcantly longer n Canada than n the U.S., by almost 5 weeks on average at the aggregate level. Ths last fndng, however, rases at least two further questons. Why does unemployment last longer n Canada? What are the relatve roles of spell duraton and spell ncdence n the unemployment rate gap between the two countres? Wth respect to the frst queston, longer unemployment spells n Canada could be due to dfferences n the composton of those becomng unemployed (that s, Canadan nflows beng more heavly weghted wth groups that tend to spend a longer tme unemployed), or to much longer spell duratons for all groups n Canada relatve to the U.S. The evdence n Table 3 suggests that the latter s the more lkely scenaro, but we formally test ths hypothess by decomposng the 15 16 17 In fact the revsed CPS questonnare, whch was mplemented n January 1994, employs a defnton of a new entrant that corresponds to the LFS defnton. Durng a parallel run of ths verson and the old verson the BLS found that n 1993 the stock share of new entrants dffered by 3.5 percentage ponts. It was 10.2% under the old questonnare, but only 6.7% under the new. See Cohany, Polvka, and Rothgreb (1994, table 8). Ths result s unchanged f we nclude a quadratc trend n the specfcaton: the cyclcal elastcty s about 0.8 n both countres. Ths s also the case for re-entrants n both countres, but ths result s dffcult to nterpret gven the measurement ssues alluded to earler. The only other elastcty sgnfcantly dfferent from the economy wde estmate s that for qutters n Canada, whch s the only estmate to be sgnfcantly greater than the overall elastcty. Analytcal Studes Branch - Research Paper Seres - 12 - Statstcs Canada No. 11F0019MPE No. 97

dfference n the economy-wde average duraton nto composton (or between group) and duraton (or wthn group) components. As mentoned n note 7, the average unemployment spell duraton n ether country can be expressed as the weghted average of group specfc duraton, where the weghts are ust the entrance shares of each group. If we let ndex countres, and ndex groups, then the average duraton s: =. (6) D () t s () t D () t Therefore, the dfference n spell duraton between the two countres (the unemployment duraton gap) can be expressed as: (7) CDN US CDN US CDN US CDN D () t D () t = ( s () t s ()) t D () t + s ()( t D () t D US ()) t. The frst term on the rght hand sde of (7) captures the part of the dfferental related to dfferences n the composton of nflows to unemployment across the two countres, whle the second term captures the part of the dfferental related to cross country dfferences n duraton wthn groups. In the frst panel of Table 5 we present the average values of each of these components over the sample perod. The dfference n the average duraton of unemployment spells measured n ths way s 4.15 weeks. 18 The decomposton reveals that roughly three quarters of the dfferental can be accounted for by cross country dfferences n spell length wthn groups. Dfferences n composton play a much smaller role. Therefore, whle a hgher proporton of unemployment spells n Canada result from employment separaton, as documented n Table 4, ths dfference n composton does not appear to be the bass for the sgnfcant dfference n aggregate duraton across the two countres. The tme seres varaton n these dfferent components s presented n fgure 1, along wth the dfference n average duraton of unemployment. The component of the duraton dfferental representng the dfference n composton across the two countres s relatvely constant over the perod, whle the component capturng the dfferences n group specfc duraton tracks the movement of the total dfferental. The composton component trends upward slghtly durng the 1981-82 recesson and durng ts mmedate aftermath, but the basc message of the fgure s that the ncrease n spell duraton for most groups n Canada drves most of the cyclcal and trend ncreases n the duraton gap. 18 Ths s smaller than the drect estmate provded n table 3 by ust over one half week. The relatonshp descrbed n equaton (6) s exact f sngle month contnuaton probabltes are used to construct estmates of average duraton. Gven that mult-month contnuaton probabltes are actually employed at the longer end of the dstrbuton, equaton (6) holds only approxmately n our data. Ths explans the apparent nconsstency between tables 3 and 5. Analytcal Studes Branch - Research Paper Seres - 13 - Statstcs Canada No. 11F0019MPE No. 97

Table 5 Analyss of the Canada - U.S. Unemployment Duraton and Unemployment Rate Dfferentals: 1980:01-1988:12 Panel A: A Decomposton of the Canada/U.S. Duraton Dfferental CDN U. S. D () t D () t CDN US.. CDN ( s ( t) s ( t)) D ( t) US.. CDN US.. s ()( t D () t D ()) t 4.15 Weeks 1.04 Weeks 3.10 Weeks Panel B: The Role of the Duraton Dfferental n Cyclcal Varaton n the Unemployment Rate Dfferental CDN U. S. (ln D ln D ) CDN (lnur U. S. ln UR ) 0.687 (0.111) Panel C: Lnear Trend Decomposton of the Unemployment Rate and Duraton Dfferentals CDN (lnur ln UR ) CDN t U. S. (ln D ln D ) t U. S. 0.0038 (0.0003) 0.0018 (0.0004) See the Appendx for data sources. Panel A: the decomposton of the aggregate duraton dfferental s outlned n equaton (7). Panel B: parameter estmate from a regresson of the cross country dfference n log duraton on season dummy varables, a lnear trend and the cross country dfference n log unemployment rates. Panel C: parameter estmates from regressons of the cross country dfferences n log unemployment rates and log duraton on season dummy varables and a lnear trend. Analytcal Studes Branch - Research Paper Seres - 14 - Statstcs Canada No. 11F0019MPE No. 97

It remans to quantfy the relatve nfluence of spell duraton and spell ncdence on the unemployment rate gap. In fact, the duraton gap and the unemployment rate gap move n tandem over much of our sample perod, and both dsplay an upward trend. Ths s clearly llustrated n fgure 2. 19 To determne the proporton of the cyclcal changes n the unemployment rate gap due to varatons n the duraton gap we regress the cross country dfference n the natural logarthm of average spell duraton on season dummy varables, a lnear trend, and the cross-country dfference n natural logarthms of the unemployment rates. The steady state dentty that the unemployment rate s the product of the ncdence rate and average spell duraton mples that the estmated parameter on the dfference n the logarthms of the unemployment rates ndcates the proportonate role of changes n average duraton. 20 The results are presented n the second panel of Table 5. The estmated elastcty suggests that close to 70% of the cyclcal varaton n the unemployment rate dfferental s due to relatve varaton n aggregate spell duraton across the two countres, versus about 30% for dfferences n spell ncdence. 21 The real puzzle of the Canada - U.S. unemployment rate gap s ts trend over tme, not ts cyclcal behavour. Wth only eght years of data we are lmted n what we can say about ths. We use a lnear trend decomposton, whch essentally nvolves drawng straght lnes through the seres plotted n fgure 2. Ths wll lkely be senstve to the choce of sample perod, but we lack the data to provde a proper senstvty analyss, or to examne longer term trends n the unemployment rate gap. A certan amount of cauton s therefore needed n acceptng ths analyss. The results of regressng the dfference n the natural logarthms of the unemployment rates on seasonal dummy varables and a lnear tme trend are presented n the frst row, thrd panel of Table 5. Trend growth n the Canadan unemployment rate exceeded the growth of ts U.S. counterpart by roughly 0.4% per month. Results from a smlar regresson of the dfference n the natural logarthms of average unemployment duraton are reported n the second row. Agan usng the steady state dentty, the estmates mply that 47% (0.0018/0.0038) of the trend ncrease n the unemployment rate gap over ths perod s accounted for by the relatvely greater growth of spell duraton n Canada. Ths result s for a very short perod of tme, but t does suggest that the reason the unemployment rate gap remaned large nto the late the 1980s has about as much to do wth the duraton of unemployment as t does wth ncdence. 19 20 21 The raw correlaton coeffcent between the two seres s 0.859. Also note that the seres for the dfference n average duraton dffer slghtly between fgure 1 and 2 for the reasons outlned n the prevous note. Fgure 2 s based on the actual average duraton data, whle fgure 1 s based on the estmate usng a weghted average of the subgroups. Our use of the steady state assumpton, dscussed n note 3 and the accompanyng text, bears repeatng. We are not suggestng that the economy was n a steady state over ths perod, rather we are undertakng a comparson of the steady states that would be mpled by the underlyng nflow and contnuaton rates. Ths specfcaton allows for dfferent seasonal and trend effects across the two countres. Specfyng common seasonal effects leads to very smlar estmates: the elastcty s 0.693 wth a standard error of 0.114. Restrctng the trend to be same n the two countres leads to an estmated elastcty of 0.557 wth a standard error of 0.069. Ths s somewhat smaller than the estmate reported n table 5, but stll mples that over half of the cyclcal varaton n the unemployment rate gap s accounted for by varaton n the duraton gap. Analytcal Studes Branch - Research Paper Seres - 15 - Statstcs Canada No. 11F0019MPE No. 97

6 Fgure 1 A DECOMPOSITION OF THE CANADA - US UNEMPLOYMENT DURATION DIFFERENTIAL Dfference n Average Duraton of Unemployment Spells 5 4 Wthn Group Duraton Component 3 Weeks 2 1 Between Group Composton Component 0-1 1980 1981 1982 1983 1984 1985 1986 1987 1988 Fgure 2 CANADA - US UNEMPLOYMENT RATE AND UNEMPLOYMENT DURATION DIFFERENCES 4 6 Canadan Unemployment Rate less US Unemployment Rate 3 2 1 Dfference n Average Duraton of Unemployment Spells Dfference n Unemployment Rates 5 4 3 Average Spell Duraton n Canada less Average Duraton n US (weeks) 0 1980 1981 1982 1983 1984 1985 1986 1987 1988 2 Analytcal Studes Branch - Research Paper Seres - 16 - Statstcs Canada No. 11F0019MPE No. 97

5. Implcatons for Explanatons of the Canada-U.S. Unemployment Rate Gap Do these fndngs contrbute to an explanaton for the gap between the unemployment rates of the two countres? The strength of our data s the nformaton t provdes on unemployment duraton, whch as we have ust ponted out may only be part of any explanaton. Nevertheless, we offer a number of stylzed facts that should be accommodated. Frst, spell ncdence and duraton appear to be equally mportant correlates of the trend ncrease n the unemployment rate dfferental over the 1980s. Second, unemployment spells tend to last much longer n Canada than n the U.S. Ths s characterstc of most groups regardless of the reason for unemployment, rather than beng a result of dfferences n composton across the two countres. Thrd, labour force entry and re-entry are more mportant sources of unemployment spells n the U.S., whle employer ntated separatons are more mportant n Canada. A complete explanaton for the Canada-U.S. unemployment rate gap has yet to be offered, but the relatvely more generous UI program n Canada s an often suggested cause. 22 Our data contan no specfc nformaton on UI recept, but t may nonetheless be of nterest to hghlght those aspects of the results that nform ths perspectve. Broadly speakng UI may nfluence the unemployment rate by changng nflows to unemployment, or by changng the duraton of spells. Addressng the matter of duraton frst, t s often argued that a larger subsdy to ob search n Canada, n the form of longer beneft enttlement, may lead to longer unemployment spells. Our results are consstent wth ths conecture, as average spell duraton s longer for most groups n Canada. On the other hand, there are lkely other dfferences between the two countres that contrbute to the duraton dfferental, and for whch we cannot control. One way to try to solate the contrbuton of the UI system n our data s to explot the fact that UI n Canada covered a broader spectrum of workers over the sample perod than t dd n the U.S. All else equal, we mght expect to fnd that the Canada - U.S. rato n average duraton s largest for groups who face larger cross country dfferences n coverage. 23 A comparson of qutters across the two countres provdes a partcularly clean vew of ths ssue. Durng the 1980s qutters were elgble to receve UI n Canada, but not n the U.S. 24 As llustrated n Table 3, the average duraton of unemployment spells among qutters s almost twce as long n Canada as t s n the U.S. In fact, the rato of average spell duratons, at 1.84, s the largest observed across all groups of the unemployed. Conversely, ndvduals experencng employer ntated unemployment spells are most lkely to be covered by UI n both countres. For permanent layoffs, the rato of average spell duraton n Canada to that of the U.S. s 1.16, one of the smallest observed, but the average duraton of temporary layoffs s actually shorter n Canada than n the U.S. As noted n the prevous secton, there may be defntonal dfferences that complcate the latter comparson. Ignorng the dstncton between a temporary and a permanent layoff abstracts from these dffcultes, and mples a rato of 1.12 for the relatve duraton of 22 23 24 A consensus on the nfluence of UI does not, however, appear to have been reached. In partcular, see Card and Rddell (1993,1995), Corak and Jones (1995), Mlbourne, Purvs and Scoones (1991), Kel and Symons (1990). Ths sort of comparson s complcated by dfferences n UI take-up rates across the two countres. Blank and Card (1991), and Storer and Van Audenrode (1993) provde evdence of trends n take-up rates for the US and Canada respectvely, whle Card and Rddell (1993) provde a cross country comparson. Recently, however, changes have been ntroduced to lmt elgblty n Canada. Analytcal Studes Branch - Research Paper Seres - 17 - Statstcs Canada No. 11F0019MPE No. 97

employer ntated separatons. 25 Taken together these comparsons would suggest that UI plays a role n determnng the duraton dfferental n the two countres, but that t s not the only factor at work. In fact, more support for ths nference comes from the duraton ratos for new entrants and re-entrants, whch are both roughly 1.45. Gven somewhat strcter requrements, t s possble that a smaller proporton of U.S. re-entrants are elgble for UI benefts. However, new entrants, usng the defnton n ether country, are unlkely to be elgble for UI, and the fact that spell duraton s also longer n Canada for ths group suggests once agan that somethng n addton to dfferences n the UI system s contrbutng to the duraton dfferental. Another possble effect of UI s that t nduces labour force partcpaton. Durng the 1980s relatvely few weeks of nsured employment were necessary for qute substantal beneft enttlement n some Canadan regons. Ths may encourage labour force partcpaton among some ndvduals leadng to relatvely short perods of employment followed by unemployment. 26 In ths way we mght expect greater churnng n the Canadan labour market. It should be stressed that we have examned evdence on the entrance shares of varous groups, not on the ncdence of unemployment. But the former can be expressed n terms of the latter n the followng way. The entrance share of group n country s equal to: (8) s N N N LF LF N (0) ( 0) = = = ( 0) ( 0) IR IR where LF represents the labour force, and IR represents the ncdence rate. Therefore, the Canada - U.S. rato of entrance shares for group s equal to: (9) s s CDN US IR IR CDN US = IR IR US CDN One of our maor fndngs s that employer ntated separatons are a larger source of unemployment n Canada (see Table 3). Equaton (9) reveals that ths could be due to a hgher ncdence of these sorts of spells n Canada, or to a hgher overall ncdence of unemployment n the U.S. Assumng that the nne year averages reported n Table 3 approxmate a steady state we can make some back of the envelope calculatons for our sample perod. Estmates of IR CDN and IR US can be obtaned by nvokng the dentty that the unemployment rate equals the product of the ncdence rate and average spell duraton. Between 1980 and 1988 the unemployment rate n Canada averaged 9.6% compared to 7.4% n the U.S. Therefore, the average weekly ncdence rate n Canada s 0.59% (9.6/16.3), whle the U.S. average s 0.64% (7.4/11.6). Thus, accordng to (9) the hgher average overall ncdence of unemployment n the U.S. durng the 1980s does contrbute to the dfference n entrance shares. Nevertheless, the Canada - U.S. rato of entrance shares of employer ntated (temporary and permanent layoff) spells s 1.23 [(0.14+0.39)/(0.18+0.25)], whle the rato of ncdence rates s 1.08 (0.64/0.59), suggestng that 25 26 Usng the average entrance shares as weghts, the average duraton of an employer ntated unemployment spells n Canada over the perod s 16.7 weeks [{(14/53)7.4} + {(39/53)20.1}]. The correspondng statstc for the US s 14.9 weeks [{(18/43)11.7} + {(25/43)17.3}]. Baker and Rea (1993), Chrstofdes and McKenna (1995), and Green and Rddell (1993) examne the effects of UI parameters on the employment hazard; the evdence n Card and Rddell (1993, 1995) s also consstent wth ths conecture. Analytcal Studes Branch - Research Paper Seres - 18 - Statstcs Canada No. 11F0019MPE No. 97