# RDP 9215: The Evolution of Employment and Unemployment in Australia 3. Gross Labour Market Flows and the Duration of Unemployment

Our analysis of gross flows begins with the identity defining the steady state, or equilibrium, unemployment rate [12],

where U is the number of people unemployed at any point in time, N is the size of the labour force at that point in time, and S is number of people who become unemployed during an interval of time, commonly known as the inflow into unemployment. Thus, we define the steady state unemployment rate to be equal to the rate at which people enter unemployment, S/N, multiplied by U/S, the average time that people remain unemployed i.e., the average duration of unemployment.

In the steady state, the outflow from unemployment, denoted H, is equal to the inflow, S. Therefore we can rewrite equation (1) as,

where H/U is the rate at which people leave unemployment i.e., the outflow rate. Thus, the equilibrium rate of unemployment at any point in time will increase either because of an increase in the inflow rate or a decrease in the outflow rate; the latter is equivalent to an increase in the average duration of unemployment.

Over any period of time, gross flows between the four states of the labour market i.e., full-time and part-time employment, unemployment and not in the labour force, can be quite large relative to the stocks of these variables, and especially large relative to the net change in the stocks. To see this, consider Table 2 which contains data on the inflows and outflows that occurred in August 1991. The table is read as follows. The entries in the rows marked FTE, for example, are the numbers of people in each of the four labour market categories this month who were in full-time employment in the previous month. The sum of the entries in the FTE rows, therefore, is total full-time employment in July 1991. The entries in the columns marked FTE are the number of people who remained in full-time employment or moved into full-time employment from part-time employment, unemployment or outside the labour force. The sum of the entries in the FTE columns, therefore, is the number of people who were employed full-time in August 1991.

From\To FTE PTE UE NILF FTE 3,084.5 51.9 42.4 36.5 PTE 52.4 207.9 19.0 28.4 UE 39.9 19.6 261.8 41.7 NILF 26.9 32.6 49.9 1,140.9 FTE 1,363.4 81.7 9.8 25.1 PTE 85.4 865.9 22.4 69.1 UE 16.1 28.0 139.5 55.0 NILF 22.8 91.5 54.8 2,333.2 Note: FTE = Full-Time Employment, PTE = Part-Time Employment, UE = Unemployed, NILF = Not in the Labour Force Source: The Labour Force : Australia, ABS Cat. No. 6203.0.

According to Table 2, 200,300 of the 601,600 people who were unemployed in July 1991 were no longer unemployed in August, either because they found employment (103,600) or left the labour force (96,700). They also show that 198,300 people became unemployed in August, either because they quit, were retrenched or otherwise left their jobs (93,600), or entered the labour force without finding a job (104,700). The net effect of these changes was a reduction in unemployment of 2,000 people, which is very small compared with the size of the flows.

Similarly, Table 2 shows that 277,400 people who were not employed in the previous month became employed in August 1991, while 252,700 people who were employed in July either became unemployed or left the labour force. The net increase in employment was therefore 24,700, again very small compared with the flows. Moreover, there were large flows within the stock of employed people: 133,600 left full-time employment and found part-time jobs, while 137,800 did the reverse.[13]

The implied stocks of employed and unemployed derived from the gross flow data will be substantially smaller than the direct (and more accurate) estimates found at the beginning of the monthly labour force survey (The Labour Force: Australia, ABS Catalogue No. 6203.0). For example, according to Table 2, there were 373,100 unemployed males in August 1991, a number found by summing the first four elements of the third column. The corresponding number in the first table of the labour force survey was 502,600.

The reason for this large discrepancy is that data on month to month flows can only be collected from respondents who are surveyed in consecutive months. However, each month one household in eight is dropped from the survey and replaced by a new household; this reduces the size of the sample from which flow data can be obtained and so increases the random sampling error of the flow estimates. What is more important, is that roughly an additional 10 per cent of respondents cannot be matched from month to month because they have moved or are no longer living in private dwellings; these people have to be excluded because they have characteristics different from the average and their inclusion would introduce a sample selection bias to the estimated flows.[14] Moreover, the number of such people varies slightly from month to month, and so the implied stocks for a given month in consecutive months are not consistent.[15]

We correct for these problems by dividing the level of each flow by the sum of the elements of each row in which it appears, as shown in Table 3. The entries in this table can be interpreted as the probability of being in a given state, conditional on being in a particular state in the previous month. Thus, for men, the probability of being in full-time employment in August 1991 if they were unemployed the previous month was 0.110. The remaining men were either employed part-time, remained in unemployment, or moved out of the labour force in August 1991. The probabilities of these events were 0.054, 0.721 and 0.115, respectively.

From\To FTE PTE UE NILF FTE 0.959 0.016 0.013 0.011 PTE 0.170 0.676 0.062 0.092 UE 0.110 0.054 0.721 0.115 NILF 0.022 0.026 0.040 0.913 FTE 0.921 0.056 0.017 0.027 PTE 0.082 0.830 0.021 0.067 UE 0.067 0.117 0.584 0.231 NILF 0.009 0.037 0.022 0.932 Note: FTE = Full-Time Employment, PTE = Part-Time Employment, UE = Unemployed, NILF = Not in the Labour Force Source: The Labour Force : Australia, ABS Cat. No. 6203.0.

In Figures 11 to 14 we plot a time series of each of the conditional probabilities illustrated in Table 2. The data run from 1981 to 1991 and are the annual averages of the monthly probabilities. The notation used is that of a conditional probability e.g., Pr(UE|FT) is the probability of being unemployed given full-time employment in the previous period.

Figure 11 shows the evolution of the conditional probabilities of moving to and from unemployment. Several interesting patterns in the data are evident:

• the probability of men moving from unemployment to full-time employment declined quite sharply during the recession of 1982–83 and, consistent with persistence in male unemployment, only recovered very slightly during the ensuing six years of strong economic growth. This probability again declined significantly during 1990 and 1991, suggesting that, if the pattern of 1984–89 is repeated during the next period of economic expansion, any decline in unemployment is likely to be modest;
• the probability of men exiting unemployment by leaving the labour force rose significantly in the period 1984–1989;
• women appear to be much more likely than men to exit from unemployment by leaving the labour force; about 25 per cent of unemployed women have done so each month. Women have also been more likely to leave unemployment by finding a part-time job, but less likely to leave unemployment by finding a full-time job;
• for both men and women, the probability of remaining unemployed from one month to the next rises sharply during recessions but falls only slowly thereafter, again consistent with persistence in unemployment. The level of the series for men is higher than for women, mainly reflecting the greater tendency of women to leave the labour force rather than stay unemployed; and
• the probability of men entering unemployment from part-time employment has varied with the unemployment cycle around an average of about five per cent, while for women, this probability has been quite stable at about two per cent. For both men and women, the probability of entering unemployment from part-time employment is greater than from full-time employment.

Figure 12 shows the conditional probabilities of moving to and from full-time employment. The major points to note are:

• the probabilities of men moving from full-time employment to another state of the labour market are small and have not moved much over time, although the probability of moving from full-time employment to part-time employment has shown a slight upward trend;
• the likelihood of women moving from full-time to part-time employment has increased over time, offsetting a fall in the probability of moving from full-time employment to outside the labour force; and
• for men, but not women, there is a clear downward trend in the likelihood of moving from part-time employment or outside the labour force to full-time employment.

In Figure 13 we plot the probabilities of moving to and from part-time employment. Note:

• the secularly declining exit rate from part-time employment to outside the labour force for women and from part-time to full-time employment for men;
• the trend increases in the likelihood of remaining in part-time employment for both men and women i.e. part-time employees are keeping their jobs for increasingly lengthy periods, perhaps reflecting the growing importance of “permanent” part-time work;
• the sharp increase, from 1984 to 1989, in the likelihood of both men and women moving from unemployment to part-time employment; and
• the trend increase in the probability of women entering part-time employment from outside the labour force. Although this increase appears to be small the implied flows, in absolute terms, are large.

Finally, in Figure 14, we plot the conditional probabilities of exiting and entering the labour force. The two top panels show the probability of entering the labour force. Of note is the increasing probability of women moving straight into the unemployment pool. The probability of remaining outside the labour force is shown in the two middle panels. Of note is the decline in this probability for women, consistent with their increased participation in the labour force.

Figures 11 to 14 suggest that the slow decline in unemployment following the 1982–83 recession was due to two factors:

• the exit rate of men from unemployment to full-time employment did not recover its pre-1982 level; and
• the increases in female employment were largely offset by the increased rates of entry of women into the labour force.

We cannot directly test whether the cause of the increase in the equilibrium rate of unemployment during the 1970s was an increase in the rate of entry to unemployment, or a decrease in the exit rate, since gross flow data do not exist for that time. However, we do have data on average duration of incomplete spells of unemployment from 1966 to 1991. They are shown in Figure 15.

This graph suggests that decreases in exit rates were the primary cause of increases in the equilibrium rate of unemployment in the mid 1970s, since average duration started to increase rapidly precisely at that time. In some respects, however, these data can give a misleading picture of the state of the labour market. For example, the average incomplete spell of unemployment can be increasing when unemployment is falling, e.g. between 1983 and 1989, when the unemployment rate fell by over four percentage points, this average increased from 37.9 weeks to 45.7 weeks. This is because exit rates from unemployment decline as the duration of unemployment increases i.e., those who leave unemployment first are generally those people who have been unemployed the least amount of time.[16] As unemployment falls, therefore, only the longer term unemployed remain, and so the average duration of the stock of existing unemployed increases. Conversely, because there were many new entrants to unemployment, average duration during the recession years 1990 and 1991 was less than in 1989.[17]

Another problem with the duration data is that some of them are wrong. For example, it is often the case that there are more people who report that they have been unemployed between 52 and 65 weeks than who, 13 weeks earlier, had been unemployed between 39 and 52 weeks, which is an arithmetic impossibility. The solution to this paradox appears to be that, when asked how long they have been unemployed, respondents to the labour force survey “cluster” their answers around six months, 12 months, 18 months etc, distorting the true duration data.[18]

One statistic less prone to these difficulties is the median duration of unemployment, shown in Figure 16. For men seeking full-time work, this duration clearly follows the unemployment cycle, as do the median durations of men looking for part-time work and women looking for full-time employment. Also of interest is the fact that the median duration of unemployment for those people searching for part-time work is significantly less than for those pursuing full-time employment. However, for men, this difference is not reflected in the differences between part-time and full-time unemployment rates. This is consistent with median male duration being much less than average duration, since it is the latter (given entry rates) which determines the equilibrium unemployment rate.

These facts confirm that, for men, long term unemployment is a serious problem. Also consistent with this suggestion is that, following the recession of 1982–83, male full-time median duration peaked only in 1985. Figure 17 shows that long term unemployment did indeed become more of a problem during the 1980s. The recession of the early 1980s led to a very large increase in long term unemployment for full-time males as a proportion of total unemployment for this group.[19]

This increase also helps explain the existence of persistence in unemployment. According to Figure 17, a recession leads to a more than proportionate increase in the number of long term unemployed. Since the long term unemployed have low exit rates, the average exit rate for all unemployed people falls in a recession, slowing any subsequent fall in the unemployment rate.

Indeed, it is possible that this persistence could permanently affect average exit rates; in other words, recessions might lead not only to temporary, cyclically high unemployment, but a higher equilibrium rate of unemployment as well. Consistent with this conclusion is the fact, shown in Figure 11, that the recession of 1982–83 led to a permanent fall in the conditional probability of unemployed men obtaining full-time employment. Other things equal, this would have permanently increased the unemployment rate of men looking for full-time work.

## Footnotes

This exposition closely follows Layard et al. (1991). [12]

These figures ought to be interpreted with some caution as they are not seasonally adjusted and labour force flows are subject to significant seasonal variation. However, the gross flows are always large relative to the net flows, regardless of the seasonal pattern. [13]

This problem has been recognised in American data by Abowd and Zellner (1985) who propose a statistical method to correct it. However, the necessary information (based on re-interviews) does not exist in Australia.
The problem is especially troublesome when the size of the labour force is revised following a census. During this time, one quarter, rather than one eighth, of the households in the survey is dropped from the sample. For this reason, the gross flow data from September to December 1987 should be treated with particular caution. [14]

For example, the data in Table 2 imply that there were 363,000 unemployed males in July 1991, a number found by summing the entries in the row marked UE. If we were to sum the UE column using flow data for July, we ought to arrive at the same total. In fact, the number is 369,000. [15]

See Fahrer and Pease (1992) for some recent evidence on the relationship between exit rates and duration of unemployment. [16]

A related problem is that the average complete duration of current spells of unemployment almost always exceeds the average duration of completed spells. This is because the former is heavily weighted by the long term unemployed. [17]

This tendency has been noted by Junankar and Kapunscinski (1990) and in American data by Akerlof and Yellen (1985). [18]

See Chapman, Junankar and Kapuscinski (1992) for a recent analysis of long-term unemployment in Australia. [19]