The Duration of Unemployment: A User Guide
Contents
1. Trivedi 1985 Estimation of Unemployment Duration from Grouped Data A Comparative Study Journal of Labor Economics Vol 3 pp 153 174 CORAK Miles 1993 The Duration of Unemployment During Boom and Bust Canadian Economic Observer Statistics Canada Catalogue No 11 010 September pp 4 1 4 20 CORAK Miles and Andrew Heisz 1994 Alternative Measures of the Average Duration of Unemployment Unpublished Report Business and Labour Market Analysis Statistics Canada 16 pp KAITZ H B 1970 Analysing the Lengths of Spells of Unemployment Monthly Labor Review Vol 93 pp 11 20 SALANT Stephen 1977 Search Theory and Duration Data A Theory of Sorts Quarterly Journal of Economics Vol 91 pp 39 57 STATISTICS CANADA 1992 Guide to Labour Force Survey Data Catalogue Number 71 5282. to overstate the average complete duration Both biases are in fact at play and it is not immediately apparent whether the average incomplete duration of unemployment overstates or understates the average complete duration a 3 The Average Complete Duration of Unemployment The new statistic introduced in this publication is the average complete duration of unemployment for a cohort of individuals that begin their spell of unemployment at the same time It is a measure of the complete length of an unemployment spell and is based upon the assumption that the economic conditions prevailing at the time a cohort becomes unemployed will continue throughout the entire spell In what follows it is referred to simply as the average complete duration of unemployment Under ideal circumstances a cohort of individuals could be followed from the month they become unemployed through their entire unemployment experience and the length of time spent unemployed noted for each individual A longitudinal survey of this sort would offer an accurate estimate of the average complete duration of unemployment but be prohibitively expensive to conduct on a regular basis However it is possible to examine the unemployment experience of a synthetic cohort of individuals that is to examine different individuals through time but individuals who as a group are representative of a single cohort A schematic representation of this procedure is offered in Figure 2
3. 4 9 17 5 1989 18 5 13 4 15 5 18 1 1990 19 1 13 8 16 4 19 8 1991 25 5 15 5 20 2 25 1 1992 26 1 18 5 21 3 25 6 1993 25 9 17 9 20 2 24 4 14 Table A 3 Average Expected Completed Duration of Unemployment By Gender and Age 1977 93 weeks Year Males Females 15 to 24 Years 25to44 Years 45 Years 1977 16 3 15 0 14 8 16 0 19 2 1978 15 8 15 1 14 0 16 4 18 9 1979 14 2 13 4 12 6 14 5 16 7 1980 15 1 13 5 13 0 15 0 18 1 1981 15 9 13 2 13 1 15 5 18 3 1982 21 7 17 5 18 0 20 7 23 5 1983 22 0 18 7 18 3 22 0 24 5 1984 18 8 16 4 14 7 19 7 22 5 1985 18 9 15 8 14 3 18 7 23 5 1986 17 3 15 0 13 3 17 5 22 2 1987 16 5 15 7 12 8 17 9 20 7 1988 15 5 14 1 11 8 16 2 19 3 1989 15 9 14 7 11 3 17 3 20 7 1990 17 0 14 8 12 6 17 4 19 7 1991 21 3 17 8 15 8 20 8 25 2 1992 22 1 19 3 15 2 22 5 28 7 1993 20 9 18 8 15 7 21 6 24 3 Table A 4 Average Expected Completed Duration of Unemployment By Educational Attainment 1977 93 weeks Year Primary Only Some Secondary or Some Post Secondary Secondary Graduation or Post Secondary l Graduation 1977 18 3 15 6 14 4 1978 17 2 15 1 15 5 1979 15 8 13 5 13 3 1980 16 8 13 9 14 1 1981 17 3 14 1 14 0 1982 20 4 19 4 20 4 1983 21 7 20 7 19 6 1984 19 4 17 4 18 2 1985 19 8 17 4 16 6 1986 18 0 16 3 15 4 1987 20 6 15 8 15 3 1988 17 8 14 4 14 8 1989 19 8 15 0 15 0 1990 18 1 14 9 17 9 1991 23 1 19 0 19 4 1992 21 9 20 2 21 5 1993 19 7 19 9 20 4 15 Bibliography BAKER G M and P K
4. The Duration of Unemployment A User Guide by Miles Corak and Andrew Heisz No 84 11F0019MPE No 84 ISSN 1200 5223 ISBN 0 660 15586 9 24 R H Coats Building Ottawa K1A OT6 Business and Labour Market Analysis Statistics Canada 613 951 9047 Internet coramil statcan ca 613 951 3748 Facsimile Number 613 951 5403 The paper is available on Internet www statcan ca December 1995 This paper represents the views of the author and does not necessarily reflect the opinions of Statistics Canada Aussi disponible en francais ABSTRACT The objective of this paper is to introduce in a new measure of the average duration of unemployment spells using Canadian data The paper summarizes the work of Corak 1993 and Corak and Heisz 1994 on the average complete duration of unemployment in a non technical way by focusing on the distinction between it and the average incomplete duration of unemployment which is regularly released by Statistics Canada It is pointed out that the latter is a lagging cyclical indicator The average complete duration of unemployment is a more accurate indicator of prevailing labour market conditions but some assumptions required in its derivation also imply that it lags actual developments Key words Unemployment Duration Dynamics Canada 1 Introduction The unemployment rate while certainly being one of the most closely watched economic indicators offers on its own a rather inco
5. The path of solid arrows leading through the darkly shaded boxes represents the unemployment experience of the cohort that became unemployed in January In each month a different group of individuals is captured by the LFS but those reporting to be unemployed for more than one month but less than two during for example February are representative of those who began their unemployment spells in January and are still unemployed the next month Similarly those reporting unemployment of more than two months but less than three in the March survey accurately represent the individuals in the January cohort who go on to experience unemployment at least that long An estimate of the average complete duration of unemployment can be calculated by noting the number of individuals in each of the darkly shaded boxes and continuing this forward tracking of the synthetic cohort until there is no one left Unfortunately this approach would not produce very timely statistics since some individuals actually experience unemployment spells that are up to two years long If this method were adopted the average complete duration of unemployment could only be produced after approximately a two year lag For example it would be determined sometime during 1993 what the complete duration of unemployment was for those individuals becoming unemployed during January 1991 Timeliness dictates that a simplifying assumption be used namely that Tn fact individuals remain
6. began in July 1981 and ended in November 1982 The Statistics Canada turning points for the recession of the 1990s have not been established but the recession most probably began in April 1990 and ended in mid 1992 10 rate fell slightly but the average duration of unemployment increased by almost 2 5 weeks If the nature of this statistic is not appreciated there is a risk of misinterpreting the information it provides Observers not aware of the fact that the average incomplete duration refers to the experience that the currently unemployed have faced not the experience that the newly unemployed will face and also not aware that changes in the average incomplete duration can be influenced by the composition of past and current inflows face the risk of misinterpreting cyclical variations in this statistic They will not recognize that it is a lagging cyclical indicator and may argue that the labour market situation is deteriorating just when it is improving as in 1993 or improving just as it is deteriorating as in 1990 In contrast the cyclical variation in the average complete duration of unemployment for those just becoming unemployed more closely resembles that of the unemployment rate which reflects the fact that this statistic is much closer to being a coincident cyclical indicator it varies with economic changes rather than lagging behind Furthermore the turning points in the movement of the statistic correspond to peaks an
7. complete duration falls between April and March by 4 6 weeks on average Similarly in the autumn the forward tracking statistic begins to lengthen between August and September increasing from 14 8 to 15 4 weeks In contrast the backward tracking statistic falls between August and September from 15 5 weeks to 12 4 weeks and only begins to increase during the next month 12 Figure 4 Average Complete Duration of Unemployment Backward Tracking and Forward Tracking Methods ra O 1 pii Co fi Backward Tracking oN Forward Tracking Average Duration weeks N 12 1 1 T 1 T 1 T 1 1 T 1 T 1 1 T 1 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 6 Conclusion No single statistic can summarize the nature of unemployment in the Canadian labour market The unemployment rate is the most watched indicator released by Statistics Canada but it needs to be supplemented with measures of the duration of unemployment This note has introduced a new measure of the average duration of unemployment the average complete duration of unemployment for a cohort of individuals that begin their spell of unemployment at the same time This statistic is a valuable complement to the average incomplete duration of unemployment for the currently unemployed that has been released regularly since 1977 A comparison of the cyclical properties of each statistic reveals that the average
8. d troughs in labour market conditions The average complete duration peaks at the same time as the unemployment rate declines during recovery and expansion and increases immediately with the onset of recession The change in this statistic during the recession of the 1990s appears to follow roughly the same path as during the 1981 82 recession The situation faced by those becoming unemployed during the early 1990s is not much different on average than that faced by those becoming unemployed a decade earlier During 1983 the average complete duration of unemployment was 20 5 weeks during 1992 it was 20 8 weeks 4 In addition to differences in cyclical variation the information in Figure 3 also illustrates that the two statistics display different levels with the average incomplete duration being longer than the average complete duration for most years Over the entire 1977 93 period the average incomplete duration is 18 7 weeks while the average complete duration is 16 6 weeks This suggests that the sampling bias outweighs the length bias It is in fact possible to obtain a complete spell measure from the average incomplete duration but like the cyclical variation of this statistic it also requires careful interpretation Under steady state conditions when the rates of both inflow to and out of unemployment are not changing the LFS will on average capture unemployment spells at their mid point Therefore the complete spell length for the curren
9. ength For example between 1981 and 1982 as the economy entered into recession the unemployment rate increased by 3 5 percentage points but the average duration increased by about only one week Similarly as the economy moved from expansion to recession between 1989 and 1990 the unemployment rate increased but the average incomplete duration actually fell Figure 3 Average Incomplete and Complete Duration of Unemployment 28 5 Unemployment Rate Right Axis 24 L 8 22 J Average Incomplete Buration Left Axis Nsa A 26 Average Duration of Unemployment weeks N Average Complete Duration Left Axis a Unemployment Rate Per Cent 1977 1979 1981 1983 1985 1987 1989 1991 1993 The pattern is just the opposite during recovery and expansion flows into unemployment fall and the stock of unemployed becomes more heavily weighted with individuals who are in the midst of rather long spells that began during the recession and reflect the state of the economy during that period Thus as recovery took hold in 1983 the unemployment rate rose by less than one percentage point but the average duration increased by about five weeks Between 1983 and 1985 expansion was well under way and the unemployment rate fell 1 5 percentage points but there was virtually no change in the average incomplete duration of unemployment Similarly between 1992 and 1993 the unemployment 3 The 1981 82 recession
10. hould not be interpreted as an indicator of current labour market conditions it does not represent the average length of time that individuals becoming unemployed can expect to spend looking for a job The objective of this note is to introduce a new statistic the average complete duration of unemployment to discuss the differences between it and the average incomplete duration and to outline the appropriate uses and limitations of each 2 The Average Incomplete Duration of Unemployment The LFS is a point in time survey it provides a snapshot of the labour market activity of a representative sample of individuals during the reference week for each month that it is conducted Such a methodology faces certain challenges when it comes to measuring the duration of time spent in a particular labour force state such as unemployment These are illustrated in Figure 1 In this figure the length of time that four different individuals spend unemployed is represented by a series of horizontal lines If a survey of these individuals were conducted at a particular point in time say January 1995 it would capture three of them while they were experiencing a spell of unemployment individuals 1 3 and 4 These individuals would report the length of their spells up to the point in time the survey 6 took place that is the lengths of the lines labeled 1 3 and 4 truncated at January 1995 Figure 1 Measuring the Duration of Unemployment from a P
11. in the LFS sample for six months with one sixth of the entire group being replaced each month The synthetic cohort approach makes no use of this rotational sample design to track individuals through time for the period that they are in the sample 8 current economic conditions remain constant for the duration of the cohort s unemployment spell This is done by comparing the number unemployed across all reported durations between adjacent surveys and is illustrated by the lightly shaded boxes in Figure 2 a backward tracking The changes in the number of unemployed along the dashed lines between the current and previous months are used to approximate the experience of the cohort currently becoming unemployed This information is used to compute the average complete duration of unemployment Figure 2 Measuring the Duration of Unemployment from a Synthetic Cohort Approach Survey Reported Duration of Unemployment months Reference Month December January February March April May June July 4 A Comparison of the Two Statistics The average complete duration of unemployment measures the length of time that individuals becoming unemployed can expect to look for a job while the average incomplete duration measures the length of time that currently unemployed individual have been looking for a job Each of this statistics has its uses but it should be stressed that the former is a more accurate indicator of prevai
12. incomplete duration is a lagging cyclical indicator while the average complete duration is much closer to being a coincident indicator Even so the derivation of the latter is based upon an assumption that causes it to lag actual developments slightly Users of LFS data may find both statistics to be of value depending upon their needs but should in all cases be aware of the limitations of each 433 Appendix Annual Figures for the Average Complete Duration of Unemployment Table A 1 Average Expected Completed Duration of Unemployment By Canada and Region 1977 93 weeks Year Canada Ontario Rest of Canada 1977 15 7 15 6 15 8 1978 15 5 15 3 15 7 1979 13 8 13 4 14 0 1980 14 3 14 2 14 5 1981 14 5 13 5 15 1 1982 19 7 19 3 20 1 1983 20 5 19 3 21 3 1984 17 8 16 2 18 6 1985 17 4 15 2 18 6 1986 16 2 14 2 17 2 1987 16 1 13 5 17 3 1988 14 8 11 8 16 2 1989 15 3 12 8 16 5 1990 16 0 15 0 16 5 1991 19 5 21 0 19 0 1992 20 8 23 0 19 7 1993 19 9 21 3 19 2 Table A 2 Average Expected Completed Duration of Unemployment By Reason for Unemployment 1977 93 weeks Year Job Leavers Labour Force Job Losers Permanent Entrants _ Layoffs 1977 19 2 13 3 16 7 21 1 1978 18 9 13 7 15 8 19 4 1979 15 9 12 4 14 2 16 9 1980 16 6 12 7 14 9 18 7 1981 16 8 12 7 15 3 18 7 1982 25 6 17 6 20 4 26 5 1983 27 4 17 9 20 9 26 3 1984 23 8 15 2 18 2 21 3 1985 22 8 14 8 17 6 20 3 1986 20 8 13 0 17 0 19 4 1987 20 3 14 3 16 0 18 6 1988 20 1 12 5 1
13. ling labour market conditions This point can be illustrated by comparing the cyclical variations in the two statistics In Figure 3 the relationship between each statistic and the Canada wide unemployment rate is illustrated using annual data from 1977 to 1993 The average incomplete duration of unemployment is slow to respond to changes in economic conditions represented in this figure by the unemployment rate with the result that the average incomplete duration measure is a lagging cyclical indicator This 2 In actual fact the previous month is used only for reported durations of one two and three months in length Sample size considerations require that the cohort be examined through increasingly wider windows of 4 to 6 months 6 months to one year and one year to about two years This requires using information from as far as one year in the past See Corak and Heisz 1994 for a more detailed explanation of the procedure 9 is in large part due to the fact that this duration measure is affected by the composition of the unemployed which changes over the business cycle At the onset of a recession large inflows into unemployment result in the stock of unemployed becoming more heavily weighted with individuals just beginning a spell of unemployment While these individuals may ultimately experience long spells of unemployment only the length of unemployment up to the time of the survey is used in calculating the average spell l
14. mplete picture of the labour market An unemployment rate of say 10 per cent may reflect a situation in which 10 per cent of the labour force becomes unemployed each month and spends only a few weeks looking for a job or a case in which the same 10 per cent of the labour force is unemployed for the entire year In the first case the labour market is characterized by a great deal of flux with a spell of unemployment not having serious consequences while in the latter it is a stagnant market with unemployment implying severe hardship The implications of these two scenarios for the well being of the unemployed are very different To accurately understand the situation requires a reliable indicator of the average duration of a spell of unemployment The design of the Labour Force Survey LFS recognizes the inherently dynamic nature of the labour market Among other things unemployed individuals are asked to report the number of weeks they have been actively looking for work The responses to this question have been used to calculate the average duration of unemployment a statistic that has been regularly released since 1977 This Statistic however could more accurately be called the average incomplete duration of unemployment because it is based upon the length of unemployment spells up to the time of the reference week This statistic is certainly valuable but it does not address all the concerns that users of the LFS may have In particular it s
15. oint In Time Survey January 1995 This makes clear that the statistic released by the LFS is a biased measure of the complete length of an unemployment spell This bias referred to as a length bias arises from the fact that the length of unemployment spells are captured only up to the time of the reference week Quite clearly then the statistic that has been released by the LFS should be interpreted as the average incomplete duration of unemployment If a length bias were the only bias in surveys of this type it would imply that the average incomplete duration of unemployment is an understatement of the average complete duration There is however another bias that works in the opposite direction This is known as a sampling bias and relates to the fact that the probability an unemployed individual will be sampled is proportional to the length of his or her unemployment spell the longer the spell the greater the chances that the individual will be included in the survey As a result those with short spells of unemployment will be underrepresented For example individual 2 in Figure 1 who experiences repeated short spells of unemployment is not included in the survey The sampling bias implies that the information used by the LFS to calculate the average duration of unemployment is over weighted with individuals who experience long spells of unemployment If this were the only bias the average incomplete duration of unemployment would tend
16. rate because it is based upon an assumption that the current situation will prevail As mentioned this assumption is required because of the lags in producing the statistic associated the forward tracking of a synthetic cohort Forward tracking is nonetheless of interest as a check on the extent of error in the backward tracking approach Figure 4 displays the annual averages of each of these statistics from 1977 onward Since the forward tracking method requires two years of future data it is only available up to 1991 The statistic derived from the backward tracking method lags that derived by the forward tracking method This is particularly so at business cycle turning points During 1981 when the 1981 82 recession began the former is three weeks shorter than the latter but during 1983 once the expansion was under way it was 2 5 weeks longer A gap of a similar magnitude 3 4 weeks also appears during 1990 the onset of another recession Thus even though the average complete duration is a more accurate indicator of current labour market conditions than the average incomplete duration it also is a slightly lagging indicator Corak and Heisz 1994 note that this caution also applies to seasonal variations The forward tracking method produces a statistic that on average falls by 3 3 weeks each March from its level in February This improvement in labour market conditions is signaled a month later by the backward tracking method the average
17. tly unemployed can be approximated by doubling the average incomplete 4 Corak 1993 points out that in spite of this unemployment has been more polarized during the recent recession the short term unemployed faring relatively better but the long term unemployed faring worse sie duration For example during the 1979 81 period the unemployment rate was steady at about 7 5 per cent This may be taken as an indication that the labour market was in a steady state The average incomplete duration of unemployment for each of those years was 14 8 14 7 and 14 9 weeks implying that the average length of an unemployment spell for those unemployed when the survey was taken of almost 30 weeks This is a very long time to be unemployed and underscores the fact that most of the total time spent unemployed economy wide is accounted for by the long term unemployed Unfortunately it is a rare occasion when the labour market is in a steady state for any extended length of time Cyclical fluctuations for example occur regularly Using this simple doubling rule will lead to an overestimate of complete duration as a recession turns into a recovery and an underestimate when an expansion turns into a recession 5 Limitations of the Average Complete Duration of Unemployment While the average complete duration of unemployment is a more accurate indicator of future labour market conditions than the average incomplete duration it may not be entirely accu
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