Unemployment Persistence, Duration Dependence, and Long-Term Unemployment: A Markov Perspective

Transcription

1 Uneployent Persistence, Duration Dependence, and Long-Ter Uneployent: A Markov Perspective by George Sheldon University of Basle Labor Market and Industrial Organization Research Unit (FAI) Abstract: This paper investigates the foral link between uneployent persistence, on the one hand, and negative dependence duration and long-ter uneployent on the other. Although negative duration dependence (iplying that the long-ter uneployed exhibit a lower re-eployent probability than the short-ter jobless) frequently appears in the literature as an explanation for the persistently high levels of uneployent in Europe, a foral link has yet to be established. Modeling uneployent as an absorbing Markov chain, we deonstrate that uneployent persistence in fact does not iply negative duration dependence, nor vice versa. Uneployent persistence does however suggest a large share of long-ter uneployed. As a result, the proportion of long-ter uneployed will perfor well in uneployent tie-series regressions, whether negative duration pertains or not. Eploying data for Switzerland, the paper reveals, in addition, that the degree of uneployent persistence is not a constant, as univariate tie-series analyses custoarily assue, but rather a function of the general level of econoic activity and the duration of uneployent insurance eligibility. Acknowledgents: This work was funded by a research grant fro the Swiss Uneployent Insurance Syste, to who we wish to express our gratitude. Thanks are also due Hans Gersbach, who provided in-depth coents on an earlier draft. I have also profited fro coents fro Nicholas Kiefer, George Neuann, and Jan van Ours. The usual caveats apply, however. Keywords: persistence, duration dependence, long-ter uneployent, Markov chain, uneployent insurance JEL-Code: C41, J64, J65 1

2 1. Introduction A close relationship between uneployent persistence, duration dependence, and long-ter uneployent has established itself in the literature in the last decade. Uneployent persistence refers to the tendency of the stock of uneployed in a nuber of European countries to reain well above pre-recession levels long after a recovery fro adverse shocks has set in. As a consequence, the tie path of uneployent in the countries affected has acquired a step-like appearance, with each successive cyclical downturn pushing uneployent up another notch. This pattern is well docuented in the literature (e.g., Alogoskoufis/Manning 1988, OECD 1994). Tie series studies of uneployent (e.g. Blanchard/Suers 1986, Barro 1988) have tried to capture this pattern by odeling uneployent as a first-order autoregressive process in which the coefficient of lagged uneployent easures the degree of persistence. One reason given in the literature for uneployent persistence is the deterioration of skills through prolonged uneployent, which worsens the uneployed s chances of regaining work (e.g., Budd et al. 1987). 1 This explanation corresponds essentially to the concept of negative duration dependence (Heckan/Borjas 198), according to which a jobless person s probability of re-eployent declines with the elapsed duration of uneployent. Negative duration dependence iplies that the long-ter uneployed have a harder tie finding work than the short-ter jobless. 2 Viewed in this way, negative duration dependence sees to provide a link between persistence and long-ter uneployent. This apparent connection has led to the use of the share of long-ter uneployed as a proxy for persistence in Beveridge curve regressions, in which the level of uneployent serves as the dependent variable (e.g., Budd et al. 1987; Christl 1988; Franz 1987; Jackan et al. 1989). In the sae vein, the OECD (1983, 1987, 1994) continually points to a positive correlation, across tie and country, between the aggregate level of uneployent and the proportion of long-ter uneployed. 1 2 Other reasons appearing in the literature are: (i) reductions in the capital stock in association with adverse shocks to eployent, which reduce the subsequent deand for labor, thereby protracting uneployent (e.g., Burda 1988) and (ii) insider-outsider structures that prevent the uneployed (outsiders) fro affecting wage-bargaining outcoes supportive of their re-eployent (e.g., Blanchard/Suers 1986). Another reason for negative duration dependence, besides the deterioration of skills, is the negative signal that long-ter uneployent sends iperfectly infored firs that use the duration of uneployent as a screening device for worker productivity (e.g., Tötsch 1988). 2

3 Despite the suggestiveness of a relationship existing between uneployent persistence, on the one hand, and duration dependence and long-ter uneployent on the other, a foral link has yet to be established. This ay be due in part to the fact that these concepts pertain to different levels of aggregation: uneployent persistence relates to the tie path of aggregate uneployent, whereas duration dependence refers to the evolution of individual joblessness. The following paper offers a odeling fraework that bridges the gap between aggregate and individual uneployent and in so doing establishes a foral relationship between persistence, duration dependence, and the share of long-ter uneployed. The approach consists in odeling uneployent as an absorbing Markov chain in which duration classes serve as the transition states through which oveent occurs, and outside-of-registered-uneployent acts as the absorbing or terinal state. Using this approach, we show that contrary to received thought, uneployent persistence does not iply negative duration dependence nor vice versa. We deonstrate that persistence does however iply a large share of long-ter uneployed, which is why the level of uneployent and the share of long-ter uneployed are found to correlate positively. As a consequence, the proportion of long-ter uneployed will perfor well in tie-series regression odels of uneployent irrespective of the presence of duration dependence. We apply the Markov approach to onthly Swiss uneployent data for the period The results confir our theoretical findings pertaining to the link between persistence, duration dependence and long-ter uneployent. Moreover, our results show that in contrast to conventional tie-series analyses of uneployent, persistence is not a paraeter of the labor arket, but rather a function of the level of econoic activity and the duration of uneployent insurance eligibility. Furtherore, we find that negative duration dependence varies positively with the business cycle, being ore pronounced in upswings than in slups. The paper unfolds as follows. Section 2 offers a stylized version of the traditional ethod of odeling uneployent persistence. Section 3 copares the Markov approach with the traditional odeling procedure and describes the foral links between persistence, duration dependence and the proportion of long-ter uneployed. Section 4 presents the results fro applying the Markov odel to Swiss data. Section 5 suarizes our results and draws policy conclusions. 3

4 2. Uneployent Persistence It is coon practice in the literature (cf. Franz 199) to odel uneployent persistence essentially as a first-order non-hoogeneous linear difference equation (1) U = ρ U + x τ τ 1 τ, in which U τ represents the stock of uneployed at tie τ, x τ denotes an exogenous variable, and ρ is a constant with range [, 1]. Fro a tie-series perspective, (1) would constitute a first-order autoregressive process with the exogenous variable x τ sybolizing a white noise or oving-average process. The coefficient ρ easures the persistence of the process iplied by (1), as it deterines the speed by which U adjusts to changes in x. To deonstrate this, we regard the tie path of U between two equilibria U * (x) and U * (x+ x), where U * (x) denotes the equilibriu 3 level of the stock of uneployed associated with level x and x represents a peranent shock to x. Fro (1) it is clear that (2) ( ) and U * x = (3) ( ) U * x+ x x 1 ρ = x + x 1 ρ. We start at tie τ = and assue that a peranent shock x occurs to x. According to (1), the level of uneployent periods later will be (4) 2 1 * ( )[ 1 ρ ρ K ρ ] ρ ( ) U = x+ x U x = ( + )( 1 ρ ) x x x ρ + 1 ρ 1 ρ. The change in the level of uneployent after periods is thus equal to the difference between (2) and (4), i.e., (5) U U * ( x ) = x 1 ( ρ ) 1 ρ 3 Asterisks denote equilibriu values. 4

5 At the end of the adjustent process, uneployent will have changed in accordance with (2) and (3) in total by * * (6) U ( x x) U ( x ) + = x 1 ρ. Thus after periods, the degree α to which adjustent is coplete equals (7) α = = 1 ρ * U U ( x) ( + ) ( ) * * U x x U x. Solving for in (7) yields (8) = ln ( 1 α) ln ρ. Hence, represents the nuber of periods required for the level of uneployent to adjust to a degree α to a new value of the exogenous variable. Observe that the size of the peranent shock x has no bearing on the value of. Equation (8) clearly deonstrates that the tie required for uneployent to adjust to any given degree α to a new equilibriu level is an increasing function of ρ across the range [, 1]. In other words, large values of ρ iply that uneployent will be slow to adjust to iproved econoic conditions, while low values iply rapid convergence. If ρ =, adjustent is instantaneous, whereas it is never-ending if ρ = 1, since in this case no unique equilibriu level of uneployent exists. This latter case is often tered hysteresis in the econoic literature, while values of ρ not greatly lower than one are denoted as persistence (cf. Wyploscz 1987). An iportant concept in regard to α is the so-called edian lag, which stes fro tie-series odels (cf., e.g., Greene 1993). The edian lag gives the nuber of periods the adjustent process takes to run 5 percent of its course, i.e., it pertains to the value assues when α equals.5. In the following, we eploy the edian lag in place of ρ as our easure of uneployent persistence. Having set out the autoregressive approach, we now contrast it with the Markov odeling procedure. 5

6 3. Absorbing Markov Chain of Uneployent Basically, a Markov chain 4 is a probabilistic odel that describes the law of oveent of a variable across a finite set of utually exclusive states in discrete tie. A Markov chain is tered absorbing if at least one state exists, the absorbing state, which can ultiately be reached fro all other states but fro which there is no escape. In our application of this odeling fraework to uneployent, we equate the non-absorbing states with uneployent duration classes and the absorbing state with non-uneployent. 5 A Markov chain of uneployent subdivides the elapsed duration of ongoing spells of uneployent into a finite set of duration classes, here defined as {(, 1], (1, 2],..., (T, T+1]}, where T sybolizes the assued longest possible spell of uneployent. The definition of the set of duration classes indicates that they have unifor width equal to one unit of process tie. We also assue that entry and exit fro uneployent occurs iediately after a period ends, so that a duration class (t-1, t] encopasses all individuals in the stock of uneployed who have been jobless for t periods. 6 The central law of otion governing an absorbing Markov chain of uneployent is given by 7 (9) U = P U 1 + N, τ τ τ where U represents a colun vector reflecting the distribution of the stock of uneployed across the T+1 duration classes defined above. N is a colun vector giving the nuber of new entries into uneployent per period. Since entry into uneployent is only possible through the lowest duration class ( 1], only the first eleent in N, which we denote by N, is non-zero. As in all Markov chains, oveent through the various states (duration classes) is governed by a square atrix P of constant transition probabilities, which in our case give an uneployed person s probability of passing fro one duration class to the Snell (1988) provides a good overview of Markov chains. By contrast, previous Markov odels of labor arket transitions have, as a rule, been non-absorbing and have pertained to different states of labor arket participation (uneployent, eployent, non-participation), as opposed to different duration classes of uneployent. See, e.g., Marston (1976), Toikka (1976) and Kiefer/Neuann (1989). Note that t pertains to duration ("age"), whereas τ refers to tie. Duration and tie are easured in identical units, however. The distinction between duration and tie should becoe apparent upon viewing (22) below. Bold letters denote atrices. 6

7 next. Since every individual oves in each period (as the width of a duration class corresponds to one unit of process tie) and then either into the next higher duration class or out of uneployent altogether, only those transition probabilities lying directly above and parallel to the ain diagonal of P are non-zero. 8 Of these, a given transition probability p(t) for t = 1,..., T gives an uneployed person s probability of passing fro duration class (t-1, t] to duration class (t, t+1], i.e., of reaining uneployed a further period, conditional on having been uneployed for t periods. In other words, the transition probabilities constitute duration-class-specific survivor rates. We assue that p() = 1 and that p(t) =, i.e., that no one enters and exits uneployent within the sae period and that no spell of uneployent lasts ore than T periods. The copleent of a survivor rate is tered its hazard rate in duration analysis. 9 The sequence of hazard rates h(t) for t = 1,..., T represents the hazard function 1 of the uneployent process in discrete tie. Duration dependence refers to the slope of the hazard function. Negative (positive) duration dependence pertains if the hazard rates decrease (increase) with increasing elapsed duration t. The situation in which h(t) does not vary across duration classes is tered the exponential case, since the hazard function of an exponential distribution is equal to a constant. Note that negative duration dependence iplies positive duration dependence with respect to survivor rates. As a coparison of (9) with (1) indicates, the essential difference between the ore conventional odeling approach of Section 2 and a Markov setting is that the latter subdivides the stock of uneployed into individual duration classes and equates the exogenous variable x to inflows into uneployent. 11 Consequently, both approaches exhibit a nuber of foral siilarities. This applies, for one, to the adjustent tie path (4). In a Markov fraework, (4) is defined in accordance with (9) as U = N+ N I+ P+ P + K + P + U N P, 2 1 * (1) [ ][ ] ( ) where I sybolizes the identity atrix and U * (N), the equilibriu duration distribution associated with inflows N. Note of course that the tie path (1) pertains to the duration class distribution of the uneployed periods after a peranent shift in the size of entering cohorts fro N to N+ N, sybolizing an exogenous shock. The first Stone (1971) investigates the properties of this particular for of the transition atrix in a deographic context. Kiefer (1988) provides a good overview of the basics of duration analysis. Behaviorally, hazard functions of uneployent can be viewed as reduced fors based on job search odels. See Devine/Kiefer (1991). Treating inflows into uneployent as exogenous is also a coon procedure in deriving the Beveridge curve fro a atching function. See, e.g., Blanchard/Diaond (1989). 7

8 ter on the right-hand side of (1) refers to the reaining stock of all cohorts that entered uneployent in the periods after tie τ =, and the second ter applies to the reaining uneployed fro the stock at tie τ =. Allowing to increase to infinity in (1) yields the equilibriu or steady-state duration class distribution of the uneployed associated with inflow level (N+ N), i.e., * (11) U ( N+ N ) = [ N+ N][ I P] 1. Note the foral siilarity between (11) and (3), the latter steing fro the conventional odeling approach. The inverse atrix [I - P] -1 in (11) is tered the fundaental atrix of a Markov chain in the literature. Due to the special diagonal structure of P, the fundaental atrix of our odel consists of an upper triangular atrix in which each row, starting at the ain diagonal, represents the conditional discrete tie survivor function 12 S(t t r- 1) of those uneployed with an elapsed duration t of at least one less than the given atrix row nuber r, i.e., (12) Stt ( r 1) = t i= r 1 j= pi () pj (). The first row of the fundaental atrix thus corresponds to the conditional survivor function for entering cohorts, i.e., the unconditional survivor function S(t), where (13) St () = t pi () i=. The survivor function S(t) gives the individual probability of reaining uneployed for at least t+1 periods. It can also be regarded as the proportion of ebers of a cohort of uneployed that can expect to reain uneployed for this duration. We intend now to derive the forula for the edian lag of our Markov chain of uneployent. In order to link the Markov odel to uneployent persistence, we concentrate on the stock of uneployed, as opposed to their distribution across dura- 12 The conditional survivor function finds use in the study of job tenure, as the area under this function corresponds to the expected rest duration of an event (i.e., holding the sae job), given that it has already lasted t periods, on which job duration studies often focus (e.g., Hall 1982). 8

9 tion classes. We begin by noting that, since only the first row of the colun vector N contains a non-zero eleent, (11) reduces to * (14) U ( N+ N ) = [ N + N][ 1 p(1) p(1)p(2) K p(1)p(2) K p(t-1)p(t) ] Hence, * ( ) ( ) * U N+ N = U N+ N e (15) ( N + N )[ 1 p(1) + p(1)p(2) + K + p(1)p(2) Kp(T-1)p(T) ] = + ( ) = N+ N Si (), T i= where e denotes the unit vector. In the exponential case, (15) siplifies essentially to (3), as in this instance all survivor rates are equal. Analogous to (15), * (16) U ( N ) = N T i= S() i, so that the total change in the steady-state level of uneployent as a result of a peranent change in the size of entering cohorts of N is equal to * * (17) ( ) ( ) U N+ N U N = N S() i T i=. Furtherore, the scalar equivalent to (1) corresponds to U = N + N S () i + N S () i (18) ( ) 1 i= T i=, iplying that * (19) ( N ) U U = N S() i. 1 i= 9

10 Thus, the degree of adjustent achieved after periods is equal to the ratio of (19) to (17), so that (2) α = * U U ( N) ( + ) ( ) * * U N N U N 1 i = = T j= Si () Sj (). As (2) indicates, the edian lag (α =.5) within a Markov odel of uneployent corresponds to that value of (nuber of adjustent periods) that divides the area under the survivor function S(t) into equal halves. This result is - to our knowledge - new in the literature. Note that the edian lag does not depend on the level of inflows into uneployent nor their changes, but rather is solely a function of survivor rates. This corresponds to the finding with respect to (8) that the size of exogenous shocks has no bearing on the value of the edian lag. Nor does the edian lag depend on the gradient of the hazard function. This becoes clear by observing that (2) reduces to (7) 13 if survivor rates do not vary across duration classes (exponential case), iplying that the general level of survivor rates are also a principle factor deterining the speed of adjustent. Hence, if the survivor rates (hazard rates) are high (low) enough on average, the tie path of uneployent will exhibit persistence whether negative duration pertains or not. In other words, negative duration dependence is not a necessary condition for uneployent persistence. Nor is it a sufficient condition, since an adequately low average survivor rate will lead to a short edian lag even in the presence of negative duration dependence. This results by no eans represents a special case. As we shall see in the next section, it is not uncoon, in fact, for the degree of negative duration dependence to fall while uneployent persistence increases. A long edian lag of uneployent adjustent does however iply a large share of long-ter uneployed. To see why, observe that, based on (15) and under the assuption that a period equals one onth, the steady-state proportion of long-ter uneployed (those uneployed with elapsed durations in excess of 12 onths) is equal to With ρ replaced by the constant survival rate p, of course. Budd et al. (1988) derive (21) without reference to Markov chains. 1

11 * (21) L T i = = 12 T j= Si () Sj (). Fro (21) it is apparent that the steady-state share of long-ter uneployed corresponds to that proportion of the area below the survivor function lying above the duration class (11, 12]. Since a long edian lag iplies that a large share of the area beneath the survivor function lies in the upper tail of the function, it also suggests a large share of long-ter uneployed. The intuition behind this result is that an exogenous change in the size of inflows into uneployent will take all the longer to work its way through the stock of uneployed the larger is the share of cohort ebers that exit uneployent fro high duration classes. Since the steady-state share of long-ter uneployed is a good proxy for the edian lag of uneployent adjustent to exogenous shocks, one should expect that the ratio of long-ter uneployed to total uneployent to perfor well in tie-series regressions of uneployent, whether duration dependence pertains or not. As a proxy for the edian adjustent lag, the share of long-ter uneployed acts uch like an error correction ter, adjusting for any short-ter deviations fro a long-run relationship between uneployent and a set of exogenous variables. 4. Case Study for Switzerland In the following we exaine the relationship between uneployent persistence, duration dependence, and long-ter uneployent epirically with respect to Switzerland for the saple period The choice of Switzerland is due to data availability. The 199s brought a sharp rise to uneployent in Switzerland. Throughout the 197s and 198s the uneployent rate rarely rose above 1 percent and stood at a ere.5 at the beginning of 199 (Figure 1). Since then, however, the uneployent rate in Switzerland has increased alost tenfold rising to nearly 5 percent by the beginning of In contrast to official practice in Switzerland, the nuerator of the uneployent rate in Figure 1 equals the su of registered uneployed and total eployed, the latter drawn fro annual national eployent statistics (Erwerbstätigenstatistik) instead of fro 1-year census figures. Our ethod of calculation yields virtually identical results up to the 199s when they begin to fall short of official figures, which ignore changes in the size of the labor force between censes. Since eployent 11

12 Figure 1: Year-Beginning Uneployent Rate, Switzerland, Percent Year The tie path of uneployent in the 199s has followed rather closely the cyclical developent of deand, as easured by the relative deviation of the seasonally and shock-adjusted onthly index of industrial production fro its trend. As Figure 2 indicates, uneployent exhibits the sae double-dip pattern as deand. Cyclical downturns in uneployent are of course not new to Switzerland. In fact, in the wake of the first oil crisis in the id 197s eployent dropped by over 8 percent, the largest decline in any OECD eber country, yet uneployent failed to reach even the 1 percent ark, the reason being that in the past a large nuber of workers exited the labor arket upon being released: foreign workers with teporary work perits returned hoe while resident workers, being uninsured against job loss, chose not to register at the eployent office and thus were not counted as uneployed. Since then, however, the situation has changed. For one, copulsory uneployent insurance coverage was introduced in April 1977 and then extended in 1984, with the enactent of the national uneployent insurance law. Secondly, the share of foreign workers with a peranent residency perit and thus the right to reain in Switzerland without a job has increased greatly. As a result of these changes, a drop in uneployent today is ore fully reflected in the uneployent statistics than in the past. has risen since 199 the official rate of 5.3 percent at the start of 1997 exceeds the 4.8 percent appearing in the chart. 12

13 Figure 2: Relative Deviation of Swiss Industrial Production 16 about Its Trend, Percent Calendar Month It is interesting to note that despite the low level of uneployent that Switzerland has enjoyed in the past, the tie path of the uneployent rate nonetheless displays the step-like pattern coon to EU eber countries, suggesting that Switzerland too has suffered fro uneployent persistence. In the following epirical investigation, we apply equations (2) and (21) to Swiss uneployent data. In order to ipleent these equations, we require survivor rates for the various duration classes. We estiate onthly survivor rates for 49 duration classes with a unifor length of one onth based on the forula 1for t = (22) pt () τ = N(t) τ N(t 1) τ 1 for t = 1, K, 47 and for t = 48, where τ = January 199,..., Deceber N(t) τ represents the nuber of uneployed in the duration class (t, t+1] on the last working day of the calendar onth τ Based on the onthly industrial production index of BAK Econoics, Basle. Equation (22) is based on the so-called life-table ethod. The forula assues that no spell of registered uneployent lasts longer than 48 onths, an assuption violated by no ore than.2 percent of all spells in our saple. Furtherore, it assues that entries in and exits fro uneployent occur on the first of each onth. This assuption siplifies calculations and has been found to be true for a ajority of uneployent spells in an earlier study (Sheldon 1989). The forula also excludes individuals who enter and exit uneployent in the sae calendar onth. In so doing, (22) underestiates the true size N() of entering cohorts, but this is iaterial for the purposes of our study. 13

14 Observe that N(t) τ and N(t-1) τ-1 refer to the sae cohort, so that (22) is based on intracohort survivor rates. The values for N(t) τ are obtained fro the onthly tapes of the coputer-based placeent and eployent statistics syste (AVAM) of the Swiss Federal Office of Industry, Trade and Labor (BIGA), which since 199 records all spells of registered uneployent in Switzerland. The values for the edian lag (2) and the share of long-ter uneployed (21) calculated on the basis of (22) constitute the steady-state values that the survivor rates of the corresponding onth iply. In the case of long-ter uneployent the steadystate values represent the level the share of long-ter uneployed would assue if the labor arket conditions that held in the particular calendar onth reained constant until equilibriu is achieved. The observed share of long-ter uneployed will lag behind the steady-state value unless labor arket conditions reain unchanged long enough for uneployent to reach its stock-flow equilibriu. Figure 3 presents the results of applying (22) to the Swiss data. The three panels present the copleents to the calculated survivor rates (i.e., their hazard rates) in the for of 12-onth averages for 199, 1993 and 1996, respectively. The panels pertain to the first 24 onths of uneployent. 18 As the figures show, the gradient of the hazard function has leveled off over the saple period, and the average hazard rate has fallen. 19 In other words, the degree of negative duration dependence 2 has declined during the econoic slup in the 199s, while the average level of survivor rates has risen. The shift of the hazard rate peak fro duration class (11, 12] in 199 to duration class (18, 19] in 1993 and 1996 has to do with changes in the axiu duration of uneployent copensation, which was extended fro 5 weeks in 199 to 6 weeks in 1992 and finally to 8 weeks in 1993 (see Sheldon 1997, for details). As a statistical test of whether the gradient of the hazard function indeed decreased, we regressed the natural logarith of the integrated hazard Λ(t) for t = 1,..., 47 on a constant and the log of duration t for the three years depicted in Figure 3. The coefficient of log duration easures the degree of duration dependence. A coefficient of 1 indicates no duration dependence, while a value below (above) 1 signifies negative As equation (15) indicates, the survivor rates of the lower duration classes are the deciding factor deterining the value of the survivor function, since they doinate in the forula. The procyclical sensitivity of the slope of the hazard function to the level of deand as pictured in Figure 3 also holds for the USA (cf. Sider 1985). The duration dependence presented in Figure 3 ay in fact reflect "heterogeneity" instead of true duration dependence (cf. Borjas/Heckan 198). The distinction is iaterial for our purposes, however. 14

15 Figure 3: Hazard Rates, Switzerland, Annual Averages Per Month Rate Elapsed Une ploy ent Duration in M onths Per Month Rate Elapsed Une ploy ent Duration in M onths Per Month Rate Elapsed Une ploy ent Duration in M onths 15

16 (positive) duration dependence. The regression results (Table 1) confir that the degree of negative duration dependence decreased in 1993 and 1996 with respect to 199. Table 1: OLS Results for ln Λ(t) = α + β ln t α -1.76*** -2.6*** *** (.31) (.26) (.22) β.827***.945***.932*** (.1) (.9) (.7) R Asterisks denote statistical significance with a risk of error of less than 1% (*), 5% (**), or 1% (***). Standard errors appear in parentheses. Despite the decrease in the degree of duration dependence, the edian lag has risen and with it - as the results in Section 3 would lead one to expect - the steady-state share of long-ter uneployed. Figure 4 shows this clearly. The tie paths presented in the diagra represent centered 5-onth oving averages of our calculated figures. As can be seen, the edian lag length increased noticeably over the saple period although the degree of negative duration dependence fell, because the general level of the hazard function fell draatically. The fact that in 199 the edian lag was low despite a high degree of negative duration dependence confirs the result fro the previous section that negative duration dependence is not a sufficient condition for uneployent persistence. And the fact that after 199 the edian lag rose although duration dependence decreased clearly deonstrates that negative duration dependence is also not a necessary for uneployent persistence. Thus, Figures 3 and 4 provide epirical support for the foral results obtained in Section 3. Furtherore, the fact that the tie path of the edian lag length closely parallels that of the steady-state share of long-ter uneployed confirs, as pointed out in the previous section, that the ratio of long-ter uneployed to total uneployent reflects, in effect, the degree of uneployent persistence. This is the reason why the share of long-ter uneployed perfors well in uneployent regression equations. But since the size of the share of long-ter uneployed can, as here, be a poor indicator of the degree of negative duration dependence, uneployent regression equations that include the share of long-ter uneployed as a right-hand variable yield inconclusive results with respect to the presence of negative duration dependence Although uneployent regression equations use the observed or, fro a Markov perspective, disequilibriu share of long-ter uneployed and not the steady-state figures appearing in Figure 4, 16

17 Figure 4: Median Lag and Long-Ter Uneployent, Switzerland, Median Lag in Months Long-Ter Share Calendar Month Median Lag Long-Ter Uneployent To link the tie path of the edian lag and the steady-state share of long-ter uneployed to the level of econoic activity and to changes in the duration of uneployent insurance eligibility, we regressed the natural logariths of the non-soothed variables appearing in Figure 4 on (i) the business cycle (CYCLE) variable presented in Figure 2, (ii) a trend, (iii) onth-specific duy variables, (iv) variables capturing the age and skill coposition of the stock of uneployed, and (v) two regie duy variables UI92 and UI93 (April 1992-Deceber 1995 and April 1993-Deceber 1995, respectively) that are intended to capture the two extensions of copensation eligibility entioned above. The results pertaining to the business cycle, trend and regie variables appear in Table 2. Table 2: Median-Lag and Long-Ter Uneployent, OLS Results, Left-Hand Variable CYCLE TREND UI 92 UI 93 DW adj. R 2 ln Long-Ter Share -7.43***.9***.41***.126*** (.68) (.2) (.71) (.6) ln Median Lag -5.49***.5***.29***.17*** (.36) (.1) (.36) (.33) Asterisks denote statistical significance with a risk of error less than 1 percent (*), 5 percent (**) or 1 percent (***). Consistent standard errors appear in parentheses. this fact does not detract fro our arguent, since the left-hand variable in uneployent regressions is also a disequilibriu value, i.e., does not correspond to, say, (16). Hence, the fact that uneployent regressions are based on disequilibriu observations iplies that the results are even less conclusive than theory alone would have one believe. 17

18 According to the results in the table, the sensitivity of the edian uneployent lag and the steady-state share of long-ter uneployed to cyclical fluctuations in econoic activity is quite high. A one percentage point fall in the relative deviation of industrial production fro its trend would increase the edian lag length by 5.49 percent and the steady-state share of long-ter uneployed by 7.43 percent. According to Figure 2, it takes roughly a half a year of trend-exceeding growth of industrial production on average to achieve a one percentage point increase in the relative deviation of industrial production fro its trend level. Viewed fro this perspective, the effects of extending uneployent insurance benefit entitleents on the length of the edian lag of uneployent adjustent and on the steady-state share of long-ter uneployed are quite substantial. Based on Table 2, the extension in 1992 raised the edian lag by 23 percent and the share of long-ter uneployed by 51 percent, while the additional extension in 1993 increased both variables by 11 percent and 13 percent, respectively. 22 The total UI-induced increase in the edian lag length and in the share of long-ter uneployed corresponds in absolute size to the effect of 1½-2 years, respectively, of trend-exceeding growth in anufacturing. In other words, the entitleent extensions had a quite substantial negative ipact on uneployent persistence. 5. Suary and Conclusions The paper has shown that, contrary to popular thinking, uneployent persistence, understood as a slow adjustent speed (edian lag) of the stock of uneployed to exogenous shocks, does not iply negative duration dependence, nor vice versa. Rather, uneployent persistence depends principally on the general level of survivor rates, not on their gradient across duration classes. Hence, negative duration dependence does not explain persistently high levels of uneployent in Europe. In fact in Switzerland, negative duration dependence declines during econoic downturns. This cyclical variability of the slope of the hazard curve iplies that proportional hazard odels, which have coe to doinate the econoetric duration analysis literature and which assue unifor proportional effects across all hazard rates, are is-specified with respect to tie-varying business-cycle variables. On the other hand, uneployent persistence does iply a large share of long-ter uneployed, the reason being that both concepts depend on the relative distribution of 22 Note that the coefficients of duy variables in a logarithic regression equation easure first differences of logs. Hence, exp(β)-1, not β, gives the percentage change of the left-hand variable in response to a regie shift. 18

19 the ass of the survivor function. If a large share of ass is concentrated in the upper tail of the survivor function, the edian adjustent lag of uneployent to exogenous shocks will be long and the steady-state share of long-ter uneployed large. Hence, the share of long-ter uneployed, acting uch like an error-correction ter, will perfor well in Beveridge regressions whether negative duration dependence holds or not. Furtherore, uneployent persistence is not a constant as autoregressive odels of uneployent iplicitly assue. Rather in the case of Switzerland, persistence varies with deand conditions and the length of uneployent benefit entitleents. In fact, the negative ipact of entitleent extensions on uneployent persistence was found to be quite substantial, corresponding in absolute ters to the effect of 1½ years of trend-exceeding growth in anufacturing. The policy iplications of our results appear rather clear-cut. In order to avoid uneployent persistence, policy easures ust be adopted that avoid long spells of uneployent. Based on our findings, long-ter entitleents to uneployent insurance benefits are counterproductive. They increase the share of long-ter uneployed, thus slowing the response of uneployent to econoic recovery. 19

20 References Alogoskoufis, G., Manning, A. (1988), "Uneployent Persistence," in: Econoic Policy, pp Barro, R., (1988), "The Persistence of Uneployent," in: Aerican Econoic Review, Papers and Proceedings, Vol. 78, pp Blanchard, O., Suers, L. (1986), "Hysteresis and the European Uneployent Proble," in: S. Fisher (ed.), Macroeconoics Annual 1986, NBER, Cabridge (Mass.), pp Blanchard, O., Diaond, P. (1989), "The Beveridge Curve," in: Brookings Papers on Econoic Activity, No.1, pp Budd, A., Levine, P., Sith, P. (1987), "Long-Ter Uneployent and the Shifting U-V Curve. A Multi-Country Study," in: European Econoic Review, Vol. 31, pp Budd, A., Levine, P., Sith, P. (1988), "Uneployent, Vacancies and the Long- Ter Uneployed," in: Econoic Journal, Vol. 98, pp Burda, M. (1988), "Is There a Capital Shortage in Europe," in: Weltwirtschaftliches Archiv, Vol. 124, pp Christl, J. (1988), "An Epirical Analysis of the Austrian Beveridge Curve," Epirica - Austrian Econoic Papers, pp Devine, T., Kiefer, N. (1991), Epirical Labor Econoics. The Search Approach, OUP, New York. Franz, W. (1987), "Hysteresis, Persistence and the NAIRU: An Epirical Analysis for the Federal Republic of Gerany," in: R. Layard, L. Calfors (eds.), The Fight against Uneployent, MIT Press, Cabridge (Mass.), pp Franz, W. (199), "Hysteresis in Econoic Relationships: An Overview," in: W. Franz (ed.), Hysteresis Effects in Econoic Models, Physica-Verlag, Heidelberg, pp Greene, W. (1993), Econoetric Analysis, 2nd edition, Macillan, New York. Hall, R. (1982), "The Iportance of Lifetie Jobs in the U.S. Econoy," in: Aerican Econoic Review, Vol. 84, pp Heckan, J., Borjas, G. (198),"Does Uneployent Cause Future Uneployent? Definitions, Questions and Answers fro a Continuous Tie Model of Heterogeneity and State Dependence," in: Econoica, Vol. 47, pp Jackan, R., Layard, R., Pissarides, C. (1989), "On Vacancies," Oxford Bulletin of Econoics and Statistics, Vol. 51., pp Kiefer, N. (1988), "Econoic Duration Data and Hazard Functions," in: Journal of Econoic Literature, Vol. 26, pp Kiefer, N., Neuann, G. (1989), Search Models and Applied Labor Econoics, CUP, Cabridge (UK). Marston, St. (1976), "Eployent Instability and High Uneployent Rates," in: Brookings Papers on Econoic Activity, , pp

21 OECD (1983), Eployent Outlook, Paris. OECD (1987), Eployent Outlook, Paris. OECD (1994), Jobs Study, Paris. Sheldon, G. (1989), Dynaik der Arbeitslosigkeit in der Schweiz, Paul Haupt Verlag, Berne/Stuttgart. Sheldon, G. (1997), "Uneployent and Uneployent Insurance in Switzerland," in: Ph. Bacchetta, W. Wasserfallen (eds.), Econoic Policy in Switzerland, Macillan, London, pp Sider, H. (1985), "Uneployent Duration and Incidence: ," Aerican Econoic Review, Vol. 75, pp Snell, L. (1988), Introduction to Probability, New York. Stone, R. (1971), Deographic Accounting and Model-Building, OECD, Paris. Toikka, (1976),"A Markovian Model of Labor Market Decisions by Workers," Aerican Econoic Review, Vol. 66, pp Tötsch, E. (1988), "Screening in Labour Markets with Heterogeneous Workers," in: R. Cross (ed.), Uneployent, Hysteresis and the Natural Rate Hypothesis, Basil Blackwell, Oxford, pp Wyploscz, C. (1987), "Coent on W. Franz: 'Hysteresis, Persistence and the NAIRU: An Epirical Analysis for the Federal Republic of Gerany'," in: R. Layard, L. Calfors (eds.), The Fight against Uneployent, MIT Press, Cabridge (Mass.), pp