reoccurrence of unemployment among adult men

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Reoccurrence of Unemployment among Adult MenAuthor(s): Mary Corcoran and Martha S. HillSource: The Journal of Human Resources, Vol. 20, No. 2 (Spring, 1985), pp. 165-183Published by: University of Wisconsin PressStable URL: http://www.jstor.org/stable/146006 .

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REOCCURRENCE OF UNEMPLOYMENT AMONG ADULT MEN

MARY CORCORAN MARTHA S. HILL

ABSTRACT

Linkages in the across-time unemployment experiences of adult men are the focus of this paper. Using Panel Study of Income Dynamics data, the paper first documents the strong persistence in unemployment for adult men. It then explores possible explanations for this persistence, searching for "scarring" effects that might remain after controlling for heterogeneity. Results strongly suggest that past unemployment does not increase adult men's chances of current unemployment, invalidating the scarring explanation. Thus, it seems safe to conclude that unemployment does not hurt adult men's chances of future employment. Apparently data collection procedures and unmeasured constant personal and environmental differences in the propensity for unemployment generated the considerable observed persistence in unemployment.

In this paper we report an investigation of whether unemployment at one period leads to later unemployment for adult men. Some research has indicated that past unemployment is at least a good predictor of subsequent unemployment among adult men. Kaitz [29], using 1965 aggregate data, showed that men's continuation rates in unemployment increased with their length of unemployment. At the micro level, Hill and Corcoran [28] found that the distribution of adult men's unemployment over a ten-year period was highly skewed, with a small group of men experiencing persistent and repeated unemployment.

There are two quite different, though not mutually exclusive, explanations for this persistence of unemployment (Kaitz [29]). Some have

Corcoran is a senior study director at the Institutefor Social Research and Associate Professor in Political Science at The University of Michigan. Hill is a senior study director at the Institute for Social Research at The University of Michigan [Manuscript received November 1982; accepted November 1984.]

The Journal of Human Resources * XX * 2 0022-166X/85/0002-0165 $01.50/0 ? 1985 by the Regents of the University of Wisconsin System



166 | THE JOURNAL OF HUMAN RESOURCES

argued that there is a feedback loop: experiencing unemployment in one period actually changes a man's likelihood of experiencing it in a later period (Phelps [36], Heckman and Borjas [26]). We will refer to this as state dependence, or the "scarring" explanation. Predictions of state dependence can be derived from both human capital and segmented labor market theories. Human capital theorists could argue that unemployment causes men to lose productivity-enhancing market experience (Phelps [36], Heckman and Borjas [26]). Segmented labor market theorists could argue that unemployment leads workers to develop poor work habits or tastes for leisure (Piore [37]), or to become typed as unreliable by future employers.

A second line of reasoning is that there are no causal links between men's past and current unemployment. Any observed association between past and current unemployment is due to differences in individuals or environments that are correlated over time and that affect men's pro- pensities for unemployment (Cripps and Tarling [11], Heckman and Bor- jas [26]). These differences in individuals' environments or characteristics that influence their propensity for unemployment will be referred to as heterogeneity. For instance, all else equal, men in areas with generous unemployment insurance or welfare plans should have higher reservation wages (McCall [32]). Similarly, workers' skills, talents, motivations, and tastes should affect expected wage offers at two points in time. It may be, for example, that some people are "losers," with attitudes, personality, or other qualities that make them undesirable workers (Heckman and Borjas [26]), or that some people are the kind who have voluntarily chosen a work package trading higher wages for more frequent layoffs (Feldstein [15]).

Past empirical work on unemployment has typically dealt with heterogeneity by including as controls a variety of measured worker and environmental characteristics. In general, such analyses show considerable serial correlation in employment behavior even after the controls for observed heterogeneity are applied. But this serial correlation may still be partly due to unobserved heterogeneity-to important, unmeasured worker and environmental characteristics which influence employment behavior and which are correlated over time. Recent empirical work on teenage unemployment (Feldstein and Ellwood [16], Ellwood [13], Corcoran [9], Meyer and Wise [33]) and on young men's unim- ployment (Heckman and Borjas [26]) shows that unmeasured-traits heterogeneity accounts for a large part of the persistence in young workers' unemployment behavior. We believe that our research, reported here, is the first attempt to test whether this holds true for prime-age male workers.

While heterogeneity and scarring are two possible reasons why adult



Corcoran and Hill i 167

men's past and current unemployment might be associated, a third possibility is that observed unemployment persistence may be an artifact of the data collection procedure. Most longitudinal surveys ask people about their unemployment over the past year. Even if there were no causal link between past and present unemployment, a single unemployment spell could look like two occurrences of unemployment by running from De- cember 31 in year t to January 1 in year t+ 1. Some of the persistence in the year-to-year patterns of unemployment might be due to "Decem- ber-January" data collection overlap problems.

We will use longitudinal data on a nationally representative sample of adult men to test whether past unemployment predicts future unemployment. This testing is done in a step-by-step manner, with each additional step allowing adjustments for factors that could obscure the true relationship between past and subsequent unemployment. First adjustments allow for individual differences which influence employment and which are constant across time (stationary heterogeneity). Then we adjust to allow for data collection problems which occur when the same spell of unemployment overlaps into two or more observation periods and spuriously inflates estimates of the relationship between past and subsequent unemployment.

The remainder of our paper is in five sections. We first describe our sample. Then we estimate unemployment persistence for this sample. This is followed by a discussion of the econometric techniques we use to examine persistence in unemployment. Next we report our empirical results using the econometric techniques to control for stationary heterogeneity and data collection problems. In the final section we sum- marize our results and their implications for employment policies.

DATA AND SAMPLE

Our sample of adult men is taken from the Panel Study of Income Dy- namics (PSID). (See Appendix A for a description of their demographic and economic characteristics.) The PSID has surveyed the economic for- tunes of a sample of 5000 American families annually since 1968 and asked the household heads in these families about their previous year's unemployment experience.1 Our sample consists of 1251 men aged 35- 64 in 1977 who were household heads and labor force participants2 every

1 The PSID initially oversampled low-income families, but the data have been weighted to correct for differential probabilities of selection.

2 Individuals were considered labor force participants if they reported themselves working, temporarily laid off, or unemployed/looking for work at the time of the interview.



168 THE JOURNAL OF HUMAN RESOURCES

year of the ten-year period 1968-1977.3 This provides information about unemployment for the period 1967 to 1976. Such prime-age male workers traditionally have lower unemployment rates than other subgroups of workers-the young and females-but constitute a large segment of the labor force, and thus their unemployment is important in the aggregate. Further, a prime-age male household head is often the primary or only earner in his family, so those who are unemployed would presumably be an important group to consider in any program designed to provide economic relief for them and their families.

PERSISTENCE IN UNEMPLOYMENT BEHA VIOR

There is considerable persistence in the unemployment behavior of adult men. Table 1 shows conditional probabilities for men's unemployment between 1972 and 1976.4 (See Appendix A for details of the unemployment patterns during this time.) This series of conditional probabilities shows a strong association between past and present unemployment. A man was 7.7 times more likely to be unemployed in 1973 if he was unemployed in 1972 than if he had experienced no unemployment in 1972 (.429 vs. .056). By 1976, a man who had been unemployed in each

TABLE 1 ESTIMATED PROBABILITY OF UNEMPLOYMENT IN YEARS 1973, 1974

1975, AND 1976 CONDITIONAL ON EMPLOYMENT STATUS IN 1972 (Sample = 1251 male heads of households aged 35-64 in 1977)

Conditional Probability of Being Unemployed Previous Employment Status 1973 1974 1975 1976

Unemployed every year .429 .500 .895 .471 from 1972 to current year

Not unemployed every year .056 .081 .054 .037 from 1972 to current year

Unemployed in 1972 .429 .440 .429 .333 Not unemployed in 1972 .056 .108 .091 .080

3 The sample was restricted to stable household heads because ten-year unemployment information was unavailable for other individuals. It was restricted to prime-age males because females and young males who were household heads over such a long period were likely to be quite unrepresentative of those who were household heads at the end of the period and because many older males retired before the end of the long-run observation period.

4 We also calculated conditional probabilities for the years 1967 to 1971; results were much the same. We restricted this analysis to five years for ease of presentation.



Corcoran and Hill 169

of the previous four years was 12.7 times more likely to report unemployment in 1976 than a man who had never been unemployed from 1972 to 1975 (.471 vs. .037).

These patterns can be misleading, however. Suppose, for instance, that unemployment spells were ten weeks long and were distributed randomly throughout the year. In that case, about one-fifth of all the unemployment spells in one year would overlap into the next. Presumably, however, overlap problems would have less effect on the probabilities of unemployment in the years 1974, 1975, or 1976 conditional on unemployment in 1972 than on the probability of unemployment in 1973 conditional on unemployment in 1972. Table 1 suggests that unemployment in 1972 was a good predictor of later unemployment-even four years later. One out of three men who reported unemployment time in 1972 also reported some unemployment in 1976, but less than one in 12 of the men who reported no unemployment in 1972 experienced any in 1976.

The pattern was similar when we examined unemployment persistence using weeks of unemployment as the unemployment measure. The comparisons were made with a simple correlation matrix for the years 1972 to 1976. Adjacent year correlations in weeks unemployed (rt,t+) were quite high-ranging from .31 (r69,70) to .47 (r75,76).5 Two years later, cross-year correlations (r,,+3) typically hovered at or below .20. After this, correlations dropped only slightly so that, for instance, the correlation between hours unemployed in the years 1967 and 1976 was .13 and that between hours unemployed in 1968 and 1976 was .22. This represented considerably more persistence than would be expected from simple overlap problems.

ECONOMIC MODELS FOR EXPLORING SOURCES OF PERSISTENCE IN MEN'S UNEMPLOYMENT

Apparent persistence in adult men's unemployment could be due to sev- eral quite distinct factors-heterogeneity, a causal impact of past unemployment on future employment stability (state dependence), or data collection procedures. We attempted to isolate the effects of such factors using techniques developed by Chamberlain [5, 6, 7] and Anderson [1] for use with sequences of binary unemployment information. These techniques allowed us to estimate measures of association between past and present unemployment while eliminating any association due either to stationary heterogeneity or to data collection procedures.

First, consider the following autoregressive logistic model which al-

5 This table can be obtained from the authors upon request.




lows for stationary heterogeneity (constant differences across individuals that affect the likelihood that they would become unemployed):

exp(a, +7yyi,- 1) (1) Prob(yit = 1 Yit-) =

1 + exp(a,+yyi,_l) where y,1 = 1 if unemployed in year t, 0 otherwise; ai = the effect of personal characteristics that influence an individual's probability of unemployment; and 7 = the degree to which unemployment last year affects the probability of unemployment this year. This equation states that the conditional probability that a man is unemployed in year t, given his unemployment status in the previous year-Prob(y1i = 11 y,,,-)-depends upon (1) a set of unmeasured personal and environmental characteristics which remain constant for that individual and have the same effect, a, on the likelihood of unemployment over the period considered, and (2) whether he was unemployed in the previous year, (Y,,t-). If these unmeasured personal characteristics completely explained unemployment persistence, then y would be equal to zero. This can be tested by con- structing a confidence interval for y.

Four features of this model should be noted. First, we are allowing for a very special sort of heterogeneity; a,i does not vary over time. That is, we assume that the effect of those individual-specific personal traits which influence the conditional probabilities of unemployment are fixed for the time period considered.6 This assumption was thought to be not too unreasonable for our sample of adult male household heads with ten- year records of labor force participation. Second, there are no Xs specified in this model.7 Effects of constant Xs are captured in ai; effects of changing Xs which are correlated over time are captured in y. Thus, this model does not allow us to separate persistence that is due to a causal relationship between past and present unemployment from persistence that is due to exogenous factors that are correlated over time (such as local demand conditions). Third, 7 is assumed to be constant over time and over individuals; that is, the effect of one year's unemployment on the next year's unemployment does not change over time and is constant for individuals. Since we concentrated the analysis on a five-year period

6 This is a strong assumption. However, most econometric techniques developed to deal with state dependence must make assumptions about the distribution of heterogeneity components in the population. These techniques facilitate estimates of the mean of y but provide no estimate of its variance.

7 This is because this model does not permit the addition of observed exogenous variables (see Chamberlain [5, 6]). Chamberlain [8] has suggested a somewhat similar model which allows for the addition of one exogenous variable. This model is discussed and used in Corcoran [9]. Note, Chamberlain [6, 7] and Heckman and Borjas [26] have developed models for use with continuous time data that do permit the addition of exogenous variables.



Corcoran and Hill 1 171

(1972 to 1976), this assumption did not appear too unreasonable for our sample of adult men. Finally, this model makes no adjustment for the way unemployment data are collected and recorded; thus our estimate of y would pick up any observed persistence in unemployment due to data collection procedures.

The next issue was to solve this model to get a consistent estimator of -. Maximizing the joint likelihood function over a,i and 7 will not provide consistent estimates. The number of individual-specific parameters, a,, to be estimated in the nonlinear form increases as the sample size increases, so that increasing sample size does not produce desired asymptotic properties. Chamberlain showed, however, that it is possible to get a consistent estimator of y if we use a conditional likelihood function. The basic idea is that the number of years a man is unemployed over the period (Si = iT YJ) and his unemployment status for the final year of observation (Yt) provide sufficient statistics for the omitted constant individual-specific factors, ai.8 We deal with initial conditions by further conditioning on unemployment status in year 1. This gives:

T

(2) Prob(yi,... ,yiT I Y, yt, Yir) t=1

T

exp(y YtYit- ) _ tt-2

T

exp(7y 2 dtd _) deBi t==2

where Bi = [d = (d,... ,d) d, = 0 or 1, d, = yil, 2,d = yiT,, dT

YiT].

For T > 4, there are conditional probabilities that depend upon y. Since not all conditional probabilities will depend upon y, this procedure uses only a subset of any given sample to estimate y. (See Appendix B for a discussion of how one estimates y.)

Suppose that y differs significantly from zero-that is, that past unemployment predicts future unemployment-even after adjusting for individual differences which affect a man's likelihood of unemployment in both periods. This finding would not allow us to conclude that a man's past and current employment are causally related because data collection and coding procedures may have generated a spurious association be-

8 This affects the distribution of a, but since we are conditioning on a, no problems arise (Chamberlain [6]).




tween past and current unemployment.9 That is, y could be nonzero simply because the same unemployment spell spans two years. If, for instance, all unemployment spells lasted ten weeks and were randomly distributed, then about one-fifth would overlap across two years.

To portray a man's unemployment history completely, we would want to know the length and timing of all spells of work and unemployment (Chamberlain [6]). If his history did not help us to predict his future, given his current state, then this is a Markov process. Chamberlain [6] termed deviations from the Markov property "duration dependence," and he pointed out that duration independence would imply that a man's unemployment history prior to the current spell should not affect the distribution of the length of the current spell, and the amount of time spent in the current spell should not affect the distribution of remaining time in that spell. This implies that the duration of the spells would be independent of each other and the distribution of time in a state would be exponential.10 If we assumed that all spells of unemployment had the same distribution, that all spells of work had the same distribution, and that the exponential rate parameter for each of the states were the same for all spells, then we would have an alternating Poisson process. In this case, the stationary heterogeneity model implies that each man's unemployment transition probabilities are characterized by the two parameters of an alternating Poisson process."' Departure from this model would be evidence of correlation between past and current chances of unemployment at the individual level; that is, even given his current state, a man's past history would help predict his future state.

Chamberlain [6] has developed tests for duration dependence using binary sequences of information on unemployment states. His techniques vary depending upon whether the data are generated by point or by interval sampling. In point sampling, men are asked to report whether they are currently unemployed; in interval sampling, men report whether they were unemployed at any time during a recent period. With point estimates of states, the technique is quite straightforward. If there is no

9 Note also that we have not taken into account effects of serially correlated exogenous factors that influence men's chances of becoming unemployed.

10 Note that this definition of duration dependence is broader than that used by Heckman and Borjas [26] and that used by Chamberlain [7]. We define duration dependence as occurring if spells of unemployment are not independent or if the amount of time spent in the current spell affects the distribution of remaining time in that spell. Cham- berlain [7] and Heckman and Borjas [26] define "duration dependence" as the second of these two possibilities. Given that we are dealing with binary unemployment histories and that we have no data on the duration of unemployment spells, we cannot estimate their narrower definition of duration dependence.

11 This is a very brief summary of an argument developed by Chamberlain in a series of papers. See Chamberlain [6, 7] for a more extensive coverage of these points.




duration dependence, then the observed binary sequences should cor- respond to a first order Markov chain. Thus, the test for state dependence reduces to a test for second (or higher) order dependence after allowing each man to have his own first order Markov chain.

For interval sampling, the test for duration dependence is more com- plex (Chamberlain [6]). The idea underlying this test is that stationary heterogeneity implies that a man's probability of being unemployed in period t depends upon the number of consecutive periods preceding period t during which he was unemployed. The reasoning goes as follows: If a man's unemployment is characterized by an alternating Poisson process, then only his unemployment state at the end of the preceding year is relevant to his status in any one year. If Yt-, = 1, we know only that he was unemployed sometime during the preceding year. We do not know whether he was unemployed at the end of the preceding year. In this case, Yt-2 could affect the probability that he was unemployed early in year t- 1 rather than late in that year; he is more likely to have been unemployed early in year t- 1 if Yt-2 = 1 than if yt-2 = 0, because of the possibility of one unemployment spell spanning both years. However, if Yt- = 0, then the man was never unemployed the previous year and thus was not unemployed at the end of that year. In this case, since we know his state at the end of year t- 1, his states in years t-2, t- 3,... would be irrelevant if his unemployment/employment process were indeed following an alternating Poisson process. This implies:

(3) Prob(yt = 1 Yt-,Y-2,.. .) = Prob(yt = Ilt-i =. . .=yt-=l, Yt-j-I =0) = Prob(yt = 1 J)

where J = the number of consecutive preceding years that the man was unemployed. That is, assuming no duration dependence and assuming an alternating Poisson process, the probability that a man is unemployed in year t depends only on how many consecutive years he was unemployed in the years immediately preceding year t. This would give the following logistic model:

(4) Probyit = 1 I Yt-i,Yit-2, exp(A)) 1 + exp(A,)

where

oo k

A, = a,i+ J ik Yit-j k- j-1

Here, each man has his own set of parameters ai and "ik which determine the nature of his Poisson distributions for time in employment and un-




employment spells. Chamberlain extended this model to test for duration dependence as follows:

1 + exp(A1+7Y2Y,t-2)

The test is based on the magnitude and significance of 72. If 72 is not significantly different from zero, then we can conclude that there is no duration dependence. That is, we can conclude that, given a man's current unemployment status, his past unemployment history has no power in predicting his future likelihood of unemployment. Chamberlain has shown that for T > 6 and large N, we can consistently estimate 72 using a conditional likelihood function. (We discuss the estimation technique in Appendix C.)

There is one important limitation to Chamberlain's technique. Chamberlain allows only for stationary heterogeneity-an unobserved, person-specific, time-invariant effect. But there may be personal or environmental characteristics which are correlated across time and which influence a man's propensity for unemployment. If the process is important, this could bias upward the estimates of state dependence or scarring. This suggests that we should be cautious about interpreting find- ings of strong state dependence based on Chamberlain's models.

EMPIRICAL RESULTS: SOURCES OF PERSISTENCE IN UNEMPLOYMENT INCIDENCE

We used Chamberlain's techniques to analyze the persistence of unemployment in our sample. We began by obtaining an estimate of first-order dependence that was based on men's binary unemployment sequences for the years 1972 to 1976 using Chamberlain's autoregressive logistic model, where each man is assigned his own unemployment probability (equations (1) and (2)). This yields 7 = 1.29 with a standard error of .36.12

Since 7 is significantly different from zero at the .01 level of confidence, we can confidently conclude that a man's unemployment in one year is a good predictor of his unemployment in the next year, allowing for stationary heterogeneity. Our estimate implies that, given that a man was unemployed in the previous year, the odds that the same man is unemployed are el 29 = 3.6 times higher than if he was not unemployed last year. While high, these odds are much lower than the odds we found when we ignored heterogeneity. Not allowing for unobserved personal

12 The details of the calculation procedure for a five-year time span (1972 to 1976) are available from the authors upon request.



Corcoran and Hill \ 175

factors that have constant effects on a worker's chances of becoming unemployed increased these odds to 12.1.'3

Applying Chamberlain's model to unemployment sequences for the period 1967 to 1971 gave similar results. The estimate of first-order dependence was smaller but still significant (' = .86 with a standard error of .30). This again suggests that past unemployment significantly predicts future unemployment, even after adjustments for stationary heterogeneity.

Recall, however, that we would expect to observe some persistence in men's unemployment behavior simply because of the way in which unemployment information is recorded. That is, past and current unemployment can be associated simply because a single unemployment spell may span two years. Instead of asking whether a man's previous year's unemployment status helps predict his current year's unemployment status, we may want to ask, given his current unemployment status, whether his prior unemployment history would enable us to predict his future chances of unemployment. That is, does unemployment behavior deviate from a Markov process?

We used information on men's eight-year unemployment sequences for the years 1969 to 1976 in conjunction with Chamberlain's procedure to assess the magnitude and significance of duration dependence (techniques based on equations (3)-(5)).14 Applying Chamberlain's model to the eight-year unemployment sequences gives an estimate of Y2 = -.25 with a standard error of .43. This point estimate is quite close to zero and has a large standard error. Given an individual's current unemployment status, his prior unemployment history is not informative about his future. Unobserved stationary heterogeneity and data collection procedures can account for the unemployment persistence observed in our sample.

SUMMARY AND CONCLUSIONS

Using data on the unemployment experiences of prime-age men from the late 1960s to the late 1970s, we investigated whether past unem-

13 We calculate these odds as follows: For each year after the first, we calculate the probability that a man was unemployed, given he was unemployed in the previous year. The average of the probabilities over years 2 to T is equal to the average value of P(l I 1). Similarly, we calculate the average value of P(1 0). For five years, these average values are .467 and .068. The odds are: ey = (.467/.533) X (.932/.068) = 12.1. Here '- would equal 2.5.

14 We use the eight-year period, 1969-1976, instead of the ten-year period, 1967-1976, because the ten-year period allowed for four times as many possible unemployment patterns as did the eight-year period. This means that the sample sizes for the unemployment patterns needed to perform the calculations were much smaller for the longer time period.




ployment leads to subsequent unemployment. A first look at simple conditional probabilities showed a strong and positive association between being unemployed at one time and the chances of being unemployed at a later date. The odds of becoming unemployed were 12 times higher for men who were unemployed last year than for men who were not unemployed. A model which adjusts for possible stationary heterogeneity- that is, differences in individuals or environments that are constant over time and affect men's chances of being unemployed-weakens but does not eliminate this association between past and later unemployment. The odds of becoming unemployed were two to four times higher if the same man were unemployed the previous year. This model, however, ignores the fact that data collection procedures (interval sampling) could generate a spurious association between men's past and current employment.

When we used a model that allows for interval sampling, we found no significant association between men's past unemployment and their subsequent unemployment. The results strongly suggest that past unemployment does not increase adult men's chances of current unemployment. Of course, we have not eliminated effects of serially correlated exogenous factors that are changing over time and that affect the likelihood of unemployment. But we suspect that ignoring effects of such exogenous factors would most likely increase estimates of state dependence.

We conclude that unemployment does not hurt adult men's chances of future unemployment. The observed persistence of unemployment found in past studies apparently is the result of data collection procedures and unmeasured constant personal differences in the propensity for unemployment.

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39. Stanley P. Stephenson, Jr. "The Economics of Youth Job Search Behavior." Review of Economics and Statistics 58 (February 1976): 104-11.

40. Finis Welch. "What Have We Learned from Empirical Studies of Unem- ployment Insurance?" Industrial and Labor Relations Review 30 (July 1977): 451-61.



Corcoran and Hill 179

APPENDIX A: CHARACTERISTICS OF THE SAMPLE AND THEIR CROSS-TIME UNEMPLOYMENT PATTERNS

As Appendix Table A-1 shows, the sample is predominantly nonblack and somewhat more concentrated in the 35-44 and 45-54 age ranges than in the 55-64 age range. The sample is about equally divided into those with less than a high school education, those with a high school education, and those with at least some college. Subjects are almost equally split between blue-collar and white-collar occupations, with a few farmers included as well. With regard to industry, durable manufacturing and trade are prominent.

APPENDIX TABLE A-i COMPOSITION OF THE SAMPLE

Subgroup Percent of Observations

Race Black 7.3 Other 92.7

Age in 1976 35-44 35.7 45-54 43.3 55-64 21.9

Education in 1976 0-8 grades 16.6 9-11 grades 14.6 12 grades 32.5 Some college 13.8 College or more 22.6

Occupation in 1976 White-collar 49.7 Blue-collar 47.0 Farmer 3.3

Industry in 1976 Agriculture/mining 5.5 Durable manufacturing 22.8 Nondurable manufacturing 7.9 Construction 7.8 Transportation/communication 8.0 Trade 13.4 Government 7.0 Other 27.5

Poverty status on average, 1967-76 Poor or near poor 2.9 Neither poor nor near poor 97.1




Appendix Table A-2 depicts the unemployment patterns for this sample for the years 1972-1976. The most frequent pattern, as would be expected, was for no unemployment over the five years; about three-quarters of the sample fell into this category. The next most frequent pattern was for one year with unemploy-

APPENDIX TABLE A-2 CROSS-TIME UNEMPLOYMENT PATTERNS, 1972-1976

Whether Unemployed Sometime During the Year (0 = no, 1 = yes)

1972 1973 1974 1

1 1 1 1 1

1

1 1

0 0 0 0 0 0

0 0 0 0

0 0

0 0 0 0

1 1 I 1 0

0 0 0 0 0 1 1

1 1 1 1 0 0 0

0 0 0 0 0

1

1

0 0 0 0

0 0 0 1

1 1

1

0 0

0 0

1 1

1 1

0 0 0 0

975 1976

1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0

Percentage of Sample

0.8 0.9 0.1 0.1 0.3 0.1 0.2 1.1 0.9 0.1 0.1 0.7 0.3 0.2 0.1 2.4 0.8 0.4 0.3 0.8 0.2 0.2 0.3 2.1 0.9 1.5 0.3 4.9 1.7 2.5 2.8

71.9




ment in the middle of the five years. This was followed in a ranking of frequency of occurrence by patterns of one year with unemployment at some other time during the period.

APPENDIX B: ESTIMATION OF THE CONDITIONAL LIKELIHOOD FUNCTION

To estimate y from equation (2), we need first to isolate all of the possible sequences of states that retain a y term as part of their conditional probability (for many, the y terms in the denominator and numerator will cancel out). The next step is to estimate y using information about the observed frequencies of this entire subset of sequences that depend on y.

Data on four or more periods are necessary to estimate y; with three or fewer periods the conditional probabilities for all possible sequences equal one. The difficulty of the task of estimating y increases with the number of periods of observation since the number of possible sequences equals 2j, where j is the number of observation periods.

For four periods, the procedure is relatively simple. Only two sets of restrictions result in conditional probabilities that retain Y as part of the probability:

4 4

[YI = O, y,= 1, y = 2] and [y, = 1, y4= O,y,t = 2] tf- t-i

For the first set:

Prob[(0011) I1 |^= O, y4 = L, yt = 2] t-1

exp{-y[(OXO) + (lXO) + (1Xl)]}

exp{y[(OXO) + (IXO) + (lXl)]} + exp{y[(lXO) + (OX1) + (1XO)]}

exp y

exp y+ 1 and

Prob[(O101) y, =O, y4 =, y2 = 2]= t-I1

exp{7[(lXO) + (OX1) + (1XO)]}

exp{'y[(OXO) + (lXO) + (1Xl)]} + exp{y[(lXO) + (OX1) + (lXO)]}

exp y+ 1 For the second set:




4 exp y Prob[(l 100) y, = 1, y4 = 0, y = 2] =

t-l exp y + 1

and

4 1 Prob[(1010) | y, = 1, y = 0, Y, = 2] =

t-l exp y + 1

Thus, we have 4 (out of a possible 16) conditional probabilities that retain y terms. The frequencies, f, attached to all 4 of these probabilities should be used to calculate y. Since

Prob[(00 11) I y, 4

= 0 Y4 = 1, z Y= t-=

= 2]

4

Prob[(O101) y, = O, y, = 1, y, = 2]

Prob[(l 100) I| y, = 1, y4 0, y, = 2] t=l

4

= 1, y4 0, Yt t--i Prob[(1010) I y, = 2]

fool 1

fool + folo fooll

foloi foioi

fooll + foloi

f1100 fJ100 + fil01 filoo

f1010 J+010

fA1oo + fiolo

we have two estimates of y: foolI/fo10, = exp(% ) and f,,oo/jf; = exp(72). We can then pool these to get a final estimate of y. To do this, we compute the weighted average of ', and A2, weighting by the inverse of their variances.

APPENDIX C: ESTIMATING DURATION DEPENDENCE

Recall Chamberlain's model:

Prob(yi, = 1 | Yit-1i,Y,t-2, ... ) exp(A, +'2y,t-2)

1 + exp(Ai+y2zi,t-2)

co k

Ai- = a, + J ti 1 yu-, k=l j=l-1

The procedure for estimating 72 is quite similar to that used for estimating Y. We eliminate the individual-specific parameters (Ai) from equations using a conditional likelihood function, and this reduces our unknowns to only one-72.

Chamberlain has shown that sufficient statistics for ai and the *ik are Sio,, Sio,i, ..., where, for example, Si,1o is the number of times in the sequence that 1 is preceded by 01. Also, we must hold the following variables fixed: yil, Yi,T-,

L

and

17

where

-

-




niT, and n1,, where ni, is the number of consecutive l's at the beginning of the sequence and niT is the number of consecutive 1's at the end of the sequence. This gives us the conditional log-likelihood function:

N T L- = ln[exp(T2 YiYi,-2)/ 2 exp(y 2 dld_-2)]

i=1 t=n11+2 debi t=ndl +2

where: B, = (d=(d, ,... ,dT) | d = 0 or 1, ndl = nil, ndT = niT, d2 = Yi2, dT- =

Yi T-1, SdOl = SiOl, Sdll = SiOll * * *)

We need T > 6 in order to generate any conditional probabilities that depend on 72.

Take the case where T = 6, a situation with 64 possible sequences. Here, one set of restrictions produces conditional probabilities that depend on Y2. This one set of restrictions yields two sequences-( 101000) and (100100). Conditional probabilities for these sequences are:

Prob[(1,0, 1,0,0,0) 1 (1,0, 1,0,0,0) or (1,0,0,1,0,0)] = 1 +exp(y2)

Prob[(l,0,0, 1,0,0) 1 (1,0, 1,0,0,0) or (1,0,0, 1,0,0)] =1 1 + exp(Y2)

We can obtain an estimate of exp(y2) by dividing the number of men with the sequence 101000 by the number of men with the sequence 100100. The natural log of the value gives us an estimate of 72-



reoccurrence of unemployment among adult men

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