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destination-specific Gamma heterogeneity uncorrelated across spells. Second, the transition intensities are not generally monotonic; an increasing then falling pattern is found for the transitions C 3 YTS, E 3 YTS and YTS 3 U. The aggregate hazard rate is non-monotonic for exits from college, employment and unemployment. Third, transition intensities for exit to college are very small for all states of origin except unemployment, where there is a sizeable intensity of transition into education at short unemployment durations. The generally low degree of transition into state C reflects the fact that, for most people, formal post-16 education is a state entered as first destination after leaving school, or not at all. However, the fact that there are unobservables common to both the initial state and transition parts of the model implies that the decision to enter college after school is endogenous and cannot be modelled separately from the transitions among the other three states. The discontinuity of exit probabilities of the two-year YTS limit is very marked (see Figure 16.7). Figure 16.8 shows the aggregated hazard rates, ! k (tjx, u)    ! k , governing exits from each state of origin, k. The typical short unemployment duration- simply a high hazard rate for exits from unemployment, but declining strongly with duration, implying a heavy right hand tail for the distribution of unemployment durations. For the other three states of origin, the hazard rates are rather flatter, except for the one- and two-year peaks for college spells. Note that we cannot distinguish unambiguously between true duration depend- ence and the effects of non-persistent heterogeneity here, at least not without imposing restrictions such as proportionality of hazards. 16.4.4. Simulation strategy The model structure is sufficiently complex that it is difficult to interpret the parameter estimates directly. Instead we use simple illustrative simulations to bring out the economic implications of the estimated parameter values. The 1.2 E 1 0.8 0.6 0.4 0.2 0 0 200 400 600 800 1000 Duration in YTS (days) Pr (exit route) Figure 16.7 Probabilities of exit routes from YTS conditional on duration. ESTIMATION RESULTS 259 `base case' simulations are performed for a hypothetical individual who is average with respect to quantitative attributes and modal with respect to most qualitative ones. An exception to this is educational attainment, which we fix at the next-to-lowest category (GCSE2), to represent the group for whom YTS is potentially most important. Thus our representative individual has the characteristics listed in Table 16.1. The treatment of state O (nonignorable attrition) is critical. We assume that, conditional on the persistent heterogeneity terms u C , u E , u U , u YTS , the labour market transition process is the outcome of a set of independent competing risks represented by the hazards ! k . Superimposed on this process is a fifth 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0 200 400 600 800 1000 Duration by state of origin (days) E C U YTS Hazard rate Figure 16.8 Aggregated hazard rates. Table 16.1 Attributes of illustrative individual. Attribute Assumption used for simulations Date of birth 28 February 1972 Ethnic origin White Educational attainment One or more GCSE passes, none above grade D Subject mix Academic mix of school subjects Health No major health problem School quality Attended a school where 38.4 % of pupils achieved five or more GCSE passes Area quality Lives in a ward where 77.9 % of homes are owner-occupied Local unemployment Unemployment rate in ward of residence is 10.3% Date of episode Current episode began on 10 March 1989 Previous YTS No previous experience of YTS Occupation When employed, is neither clerical nor craft/technical Special needs Has no special training needs when in YTS 260 HETEROGENEOUS TRANSITION MODELS IN LABOUR ECONOMICS independent risk of attrition which is relevant to the observation process but irrelevant to the labour market itself. In this sense, attrition is conditionally ignorable, by which we mean that it is independent of the labour market transition process after conditioning on the persistent unobservables. It is not unconditionally ignorable since the unobservables generate correlation between observed attrition and labour market outcomes, which would cause bias if ignored during estimation. However, conditional ignorability means that, once we have estimated the model and attrition process jointly (as we have done above), we can nevertheless ignore attrition in any simulation that holds fixed the values of the persistent unobservables. In these circumstances, ignor- ing attrition means marginalising with respect to the attrition process. Given the assumption of conditional independence of the competing risks, this is equivalent to deleting all hazards for exit to state O and simulating the remaining four-risk model. This procedure simulates the distribution of labour market event histories that would, if unhampered by attrition, be observed in the subpopulation of individuals with heterogeneity terms equal to the given fixed values u k . The simulation algorithm works as follows. For the representative individual defined in Table 16.1, 500 five-year work histories are generated via stochastic simulation of the estimated model. 1 These are summarised by calculating the average proportion of time spent in each of the four states and the average frequency of each spell type. To control for endogenous selection and attrition, we keep all the random effects fixed at their median values of zero, and reset all transition intensities into state O to zero. We then explore the effects of the covariates by considering a set of hypothetical individuals with slightly differ- ent characteristics from the representative individual. These explore the effects of ethnicity, educational attainment and the nature of the locality. For the last of these, we change the SCHOOL, AREA and URATE variables to values of 10%, 25% and 20% respectively. Table 16.2 reveals a large impact for the variables representing ethnicity and educational attainment, in comparison with the variables used to capture the influence of social background. An individual identical to the base case, but from a non-white ethnic group (typically South Asian in practice), is predicted to have a much higher probability of remaining in full-time education (59 % of the five-year period on average, compared with 20 % for the reference white individual). However, for ethnic minority individuals who are not in education, the picture is gloomy. Non-whites have a much higher proportion of their non- college time (22 % compared with 9 %) spent unemployed, with a roughly comparable proportion spent in YTS. The effect of increasing educational attainment at GCSE is to increase the proportion of time spent in post-16 education from 20 % to 31 % and 66 % for the three GCSE performance classes used in the analysis. Improving GCSE 1 The simulation process involves sampling from the type I extreme value distribution for the logit parts of the model, and from the distribution of each latent duration for the transition part. In both cases, the inverse of the relevant cdf was evaluated using uniform pseudo-random numbers. ESTIMATION RESULTS 261 Table 16.2 Simulated effects of the covariates for a hypothetical individual. Simulated individual Spell type Proportion of time (%) Proportion of non-college time Frequency of spells (%) Mean no. of spells Base case C 19.7 Ð 18.2 (see Table 16.1) E 56.9 70.9 39.0 2.59 U 7.2 9.0 24.1 YTS 16.2 20.2 18.7 Non-white C 58.7 Ð 55.3 E 24.2 58.6 17.8 2.01 U 9.3 22.5 18.8 YTS 7.8 18.9 8.0 1±3 GCSEs at grade C or better C 30.6 Ð 29.9 E 47.7 68.7 33.1 2.16 U 9.3 13.4 23.2 YTS 12.4 17.9 13.8 More than 3 GCSEs at grade C or better C 65.6 Ð 64.8 E 24.3 70.6 17.2 1.55 U 4.5 13.1 12.0 YTS 5.6 16.3 6.0 Major health problem C 22.2 Ð 21.3 E 52.4 67.4 33.6 2.57 U 4.8 6.2 22.3 YTS 20.6 26.5 22.8 Poor school and area quality C 18.4 Ð 17.0 E 52.8 64.7 35.9 2.75 U 9.1 11.2 24.4 YTS 19.6 24.0 22.7 Note: 500 replications over a five-year period; random effects fixed at 0. performance has relatively little impact on the amount of time predicted to be spent in unemployment and its main effect is to generate a substitution of formal education for employment and YTS training. There is a moderate estimated effect of physical and social disadvantage. Individuals identified as having some sort of (subjectively defined) major health problem are predicted to spend a greater proportion of their first five post-school years in college or YTS (43 % rather than 36 %) compared with the otherwise similar base case. This displaces employment (52 % rather than 57 %), but also reduces the time spent unemployed by about two and a half percentage points. In this sense, there is evidence that the youth employment system was managing to provide effective support for the physically disadvantaged, if only temporarily. After controlling for other personal characteristics, there is a significant role for 262 HETEROGENEOUS TRANSITION MODELS IN LABOUR ECONOMICS local social influences as captured by the occupational, educational and housing characteristics of the local area, and the quality of the individual's school. Poor school and neighbourhood characteristics are associated with a slightly reduced prediction of time spent in college and employment, with a corresponding increase in unemployment and YTS tenure. Nevertheless, compared with race and education effects, these are minor influences. 16.4.5. The effects of unobserved heterogeneity To analyse the effects of persistent heterogeneity specific to each state of origin, we conduct simulations similar to those presented in the previous paragraph. The results are shown in Figures 16.9±16.12. We consider the representative individual and then conduct the following sequence of stochastic simulations. For each state k  C, E, U, YTS set all the heterogeneity terms to zero except for one, u k , whose value is varied over a grid of values in the range [À2, 2] (covering approximately four standard deviations). At each point in the grid, 500 five-year work histories are simulated stochastically and the average pro- portion of time spent in each state is recorded. This is done for each of the four u k , and the results plotted. The plots in Figures 16.9±16.12 show the effect of varying each of the heterogeneity terms on the proportion of time spent respectively in college, employment, unemployment and unemployment. 25% 20% 15% 10% 5% 0% −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 Value of random effect Proportion of time in college C E U YTS Figure 16.9 The effect of each state-specific random effect on the proportions of time spent in college. ESTIMATION RESULTS 263 80% 70% 60% 50% 40% 30% 20% 10% 0% −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 Proportion of time in employment Value of random effect C E U YTS Figure 16.10 The effect of each state-specific random effect on the proportions of time spent in employment. 12% 10% 8% 6% 4% 2% 0% −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 Proportion of time in unemployment Value of random effect C E U YTS Figure 16.11 The effect of each state-specific random effect on the proportions of time spent in unemployment. The striking feature of these plots is the large impact of these persistent unobservable factors on the average proportions of the five-year simulation period spent in each of the four states. This is particularly true for college, 264 HETEROGENEOUS TRANSITION MODELS IN LABOUR ECONOMICS 25% 20% 15% 10% 5% 0% −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 Proportion of time in YTS Value of random effect C E U YTS Figure 16.12 The effect of each state-specific random effect on the proportions of time spent in YTS. where the proportion of time spent in education falls from over 20 % at u C  0 to almost zero at u C  2, with a corresponding rise in the time spent in employment and unemployment. The proportion of time spent unemployed (essentially the unemployment rate among individuals of the representative type) is strongly influenced by all four state-specific random effects, with a 6 percentage point variation in the unemployment rate. 16.5. SIMULATIONS OF THE EFFECTS OF YTS simulations ofthe effects of yts We now bring out the policy implications of the model by estimating the average impact of YTS for different types of individual, again using stochastic simulation as a basis (Robins, Greenland and Hu (1999) use similar tools to estimate the magnitude of a causal effect of a time-varying exposure). A formal policy simulation can be conducted by comparing the model's predictions in two hypothetical worlds in which the YTS system does and does not exist. The latter (the `counterfactual') requires the estimated model to be modified in such a way that YTS spells can no longer occur. The results and the interpretational problems associated with this exercise are presented in Section 16.5.2 below. However, first we consider the effects of YTS participation and and of early dropout from YTS, by comparing the simulated labour market experience of YTS participants and non-participants within a YTS world. For this we use the model as estimated, except that the `risk' of attrition (transition to state O) is deleted. SIMULATIONS OF THE EFFECTS OF YTS 265 16.5.1. The effects of YTS participation We work with the same set of reference individuals as in Sections 16.4.4±16.4.5 above. Again, the state-specific random effects are fixed at their median values of 0, so that the simulations avoid the problems of endogenous selection arising from persistent unobservable characteristics. This time the 500 replications are divided into two groups: the first one contains histories with no YTS spell and the second one histories with at least one YTS spell. We have then two groups of fictional individuals, identical except that the first happen by chance to have avoided entry into YTS, while the second have been through YTS: thus we compare two potential types of work history, only one of which could be observed for a single individual (Holland, 1986). To make the comparison as equal as possible, we take the last three years of the simulated five-year history for the non-YTS group and the post-YTS period (which is of random length) for the YTS group. We exclude from each group those individuals for whom there is a college spell in the reference period, thus focusing attention solely on labour market participants. Figure 16.13 shows, for the base case individual, the difference in simulated unemployment incidence for the two groups. At the median value of the random effects, the difference amounts to approximately 5 percentage points, so that YTS experience produces a substantially reduced unemployment risk. We have investigated the impact of unobservable persistent heterogeneity by repeating the simulations for a range of fixed values for each of the u k . Figure 16.13 shows 14% 10% 12% 8% 6% 4% 2% 0% −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 Proportion of time unemployed Unemployment-specific random effect YTS spell No YTS spell Figure 16.13 The proportions of labour market time spent unemployed for individuals with and without YTS episodes. 266 HETEROGENEOUS TRANSITION MODELS IN LABOUR ECONOMICS the plot for u U ; broadly similar patterns are found for the other u k , suggesting that the beneficial effect of YTS participation is more or less constant across individuals with differing unobservable characteristics. Table 16.3 shows the influence of observable characteristics, summarising the results of simulations for the base case and peturbations with respect to ethni- city, education and area/school quality. The beneficial effects of YTS partici- pation are evident in all cases, but are particularly strong for members of ethnic minorities and for those with better levels of school examination achievement. Note that these are the groups with the highest probabilities of full-term YTS spells. 16.5.2. Simulating a world without YTS The ultimate aim of this type of modelling exercise is to say something about the economic effects of implementing a training/employment subsidy scheme such as YTS. The obvious way to attempt this is to compare simulations of the model in two alternative settings: one (the `actual') corresponding to the YTS scheme as it existed during the observation period; and the other (the `counter- factual') corresponding to an otherwise identical hypothetical world in which YTS does not exist. There are well-known and obvious limits on what can be concluded from this type of comparison, since we have no direct way of knowing how the counterfactual should be designed. Note that this is not a Table 16.3 Simulated effects of YTS participation on employment frequency and duration for hypothetical individuals. Replications with no YTS spell Simulated individual % period in work % spells in work Base case 89.9 86.0 Non-white 65.3 60.5 1±3 GCSEs at grade C 85.1 83.0 b 3 GCSEs at grade C 88.3 85.4 Low school and area quality 86.5 84.0 Replications containing a YTS spell Simulated individual % post-YTS period in work % post-YTS spells in work Mean YTS duration % YTS spells full term Base case 95.1 89.2 1.47 51.0 Non-white 86.6 80.2 1.56 59.5 1±3 GCSEs at grade C 96.5 91.8 1.62 63.6 b 3 GCSEs at grade C 98.6 96.8 1.75 73.1 Low school and area quality 90.1 81.1 1.47 51.8 Note: 500 replications over a five-year period; random effects fixed at 0. SIMULATIONS OF THE EFFECTS OF YTS 267 problem specific to the simulations presented in this chapter; any attempt to give a policy-oriented interpretation of survey-based results is implicitly subject to the same uncertainties. The design of a counterfactual case requires assumptions about three major sources of interpretative error, usually referred to, rather loosely, as deadweight loss, displacement and scale effects. Deadweight loss refers to the possibility that YTS (whose objective is employment promotion) may direct some re- sources to those who would have found employment even without YTS. Since YTS has some of the characteristics of an employment subsidy, this is a strong possibility. It seems likely that if YTS had not existed during our observation period, then some of those who were in fact observed to participate in YTS would have been offered conventional employment instead, possibly on old-style private apprenticeships. Displacement refers to a second possibility that a net increase in employment for the YTS target group might be achieved at the expense of a reduction in the employment rate for some other group, presumably older, poorly qualified workers. Note, however, that displacement effects can also work in the other direction. For example, Johnson and Layard (1986) showed, in the context of a segmented labour market with persistent unsatisfied demand for skilled labour and unemployment amongst unskilled workers, that training programmes can simultaneously produce an earnings increase and reduced unemployment probability for the trainee (which might be detected by an evaluation study) and also make available a job for one of the current pool of unemployed. A third interpretative problem is that the aggre- gate net effect of a training programme may be non-linear in its scale, so that extrapolation of a micro-level analysis gives a misleading prediction of the effect of a general expansion of the scheme. This mechanism may work, for instance, through the effect of the system on the relative wages of skilled and unskilled labour (see Blau and Robins, 1987). The evidence on these effects is patchy. Deakin and Pratten (1987) give results from a survey of British employers which suggests that roughly a half of YTS places may have either gone to those who would have been employed by the training provider anyway or substituted for other types of worker (with deadweight loss accounting for the greater part of this inefficiency). However, other authors have found much smaller effects (see Jones, 1988), and the issue remains largely unresolved. Blau and Robins (1987) found some empirical evidence of a non-linear scale effect, by estimating a significant interaction between programme size and its effects. The need for caution in interpreting the estimated effects of YTS participation is evident, but there exists no clear and simple method for adjusting for deadweight, displacement and scale effects. The economic assumptions we make about the counterfactual have a direct parallel with the interpretation of the statistical transition model (see also Greenland, Robins and Pearl (1999) for a discussion on this). To say anything about the effects of removing the YTS programme from the youth labour market requires some assumption about how the statistical structure would change if we were to remove one of the possible states. The simulations we present in Table 16.4 correspond to the very simplest counterfactual case and, 268 HETEROGENEOUS TRANSITION MODELS IN LABOUR ECONOMICS [...]... À0.666 (0.20) À1.233 (0.24) À2.046 (0.26) À0.642 (0.39) 4. 782 (0.59) Ð 2 .85 3 (0.41) Ð À0.690 (0.47) À1.6 28 (0.51) À2.630 (2.62) À6.926 (0. 78) 0.795 (0.11) Ð À0.1 98 (0.17) Ð Ð Ð Ð Ð Ð Ð À1.115 (0.33) À2.221 (0.32) Ð À0.962 (0.61) 5.079 (0. 58) Ð 1.197 (0.36) À1. 389 (0.45) Ð 8. 488 (3.32) À4. 481 (1.11) À1 .88 4 (0.14) Ð Ð Ð Ð Ð Ð Ð 1.007 (0.29) 0.437 (0. 18) À1.036 (0.45) À1.642 (0.45) 0.964 (0.75) 3.469 (1.05)... efforts in constructing the database used in this study Pinuccia Calia provided valuable research assistance We received helpful comments from seminar participants at the Universities of Florence and Southampton Analysis of Survey Data Edited by R L Chambers and C J Skinner Copyright 2003 John Wiley & Sons, Ltd ISBN: 0-471 -89 987 -9 PART E Incomplete Data Analysis of Survey Data Edited by R L Chambers... where the sum of the imputed residuals ~t is zero Obviously, under this type r of imputation the variance of the imputed mean and the variance of the regression estimator are the same, and no efficiency is lost by adopting an imputation-based approach to estimation  286 17.5 INTRODUCTION TO PART E COMBINING SURVEY DATA AND AGGREGATE DATA IN ANALYSIS combining survey data and aggregate data in analysis Many... straightforward one where unit-level data on W and Z, along with group identifiers, are available to the more challenging situation where the survey data just consist of group-level sample averages of W and Z In the former case S can be estimated via substitution of estimates for the parameters COMBINING SURVEY DATA AND AGGREGATE DATA IN ANALYSIS 287 of the right hand side of (17.4) obtained by using a multilevel... of a major health problem SCHOOL Measure of school quality ˆ proportion of pupils with at least 5 GCSE passes in first published school league table AREA Measure of social background ˆ proportion of homes in ward of residence that are owner-occupied Spell-specific variables (mean over all episodes): DATE Date of the start of spell (years since 1 January 1 988 ) YTSYET Dummy for existence of a spell of. .. of inference for sample surveys In this chapter I apply this perspective to the analysis of survey data subject to unit and item nonresponse I first extend the Bayesian modeling framework of Chapter 4 to allow for missing data, by adding a model for the missing -data mechanism In Section 18. 2, I apply this framework to unit nonresponse, yielding Bayesian extensions of weighting methods In Section 18. 3,... 0.9 5.5 10.1 70.3 62.9 0.7 2.5 Marginal 3.1 21.5 9.7 20.2 5.1 40.5 100 Marginal Marginal 47.4 10.6 28. 2 13 .8 (b) All spells Destination state State of origin C E U YTS Attrition Incomplete C E U YTS Ð 0.7 5.3 1.3 8. 1 Ð 37 .8 70.6 13.4 13.2 Ð 16.5 4.9 5 .8 41.2 Ð 4 .8 0.4 13.3 8. 2 68. 8 79.9 2.4 3.4 Marginal 1 .8 25.3 10.7 13.1 6.2 42.9 Table A3 25.1 30.5 24.5 19.9 100 Mean durations (years) C Table A4 U YTS... À1.919 (0.77) 2.150 (0.61) 2.369 (0 .88 ) 3.406 (0.94) Ð Ð 5.530 (0.73) Ð À0.447 (0.72) Ð 1.512 (1.23) Ð À5.924 (0.57) Ð Ð 0.762 (0. 18) À2.5 68 (0.71) Ð Ð Ð À0.335 (0.15) 1.433 (0. 28) Ð À0.700 (0.17) À0.939 (0. 18) Ð Ð 6.654 (0.54) 3.5 58 (0.49) 0.927 (0.22) 0.233 (0.32) Ð À3.231 (1.99) À1 .82 0 (0.71) Ð 1.461 (0.43) À1.3 28 (0.46) À3.234 (0.75) À0.610 (0.50) À0 .86 5 (0.53) 1.1 58 (0.41) Ð À0.751 (0.32) À0.666 (0.20)... for different numbers of units because of attrition The three chapters making up Part E of this book explore survey data analysis where relevant data are, in one way or another, and to different extents, missing The first, by Little (Chapter 18) , develops the Bayesian approach to inference in general settings where the missingness arises as a consequence of different forms of survey nonresponse In... of population covariates zu and the (unobserved) `complete' sample data matrix ys , of the matrix of sample nonresponse indicators rs generated by the survey nonresponse mechanism, be the same as that of the conditional distribution of this outcome given zu and the observed sample data yobs Like the noninformative nonresponse assumption, it allows a useful factorisation of the joint distribution of . spells Base case C 19.7 Ð 18. 2 (see Table 16.1) E 56.9 70.9 39.0 2.59 U 7.2 9.0 24.1 YTS 16.2 20.2 18. 7 Non-white C 58. 7 Ð 55.3 E 24.2 58. 6 17 .8 2.01 U 9.3 22.5 18. 8 YTS 7 .8 18. 9 8. 0 1±3 GCSEs at grade. À1.377 (1 .85 ) À5.924 (0.57) À1 .82 0 (0.71) À6.926 (0. 78) À4. 481 (1.11) DATE 8. 090 (2.99) Ð Ð 0.795 (0.11) À1 .88 4 (0.14) YTSYET Ð Ð 1.461 (0.43) Ð Ð YTSDUR Ð 0.762 (0. 18) À1.3 28 (0.46) À0.1 98 (0.17). in work % spells in work Base case 89 .9 86 .0 Non-white 65.3 60.5 1±3 GCSEs at grade C 85 .1 83 .0 b 3 GCSEs at grade C 88 .3 85 .4 Low school and area quality 86 .5 84 .0 Replications containing a YTS