Notes

^1.

For recent examples and discussion of this work see Finnie et al. (2008, 2010).

^2.

Full-time enrollments in undergraduate programs in Canada were 481,053 in 1995/96 and 654,403 in 2007/08 (CANSIM Table 477-0013).

^3.

As of 31 October 2006 (the most recent year for which data are available), there were 428,805 full-time students enrolled in college programs leading to college certificates or diplomas, post-diploma programs, collaborative degree programs, university transfer programs, and college preliminary year courses. See CANSIM Table 477-0015.

^4.

Admittedly, this is a rather rough calculation of completion rates. In the PSE literature, it is common to use longitudinal data to calculate completion rates. These data allow researchers to track individuals over time and so actual program length can be calculated from program start and end dates. Then, a completion rate can be calculated by dividing the number of number of completers in a cohort by the number of entrants in that same cohort. Unfortunately, these data are not currently available. Given the increase in the number of entrants over this 12-year period (Table 1), coupled with the time it may take to complete a program, readers may wonder whether the completion rates as calculated in Table 2 underestimate the true completion rates. The likely answer is yes, although the growth in the number of completions is still only about one-third as large as the 120% increase in the total number of registrations (Table 1). The raw data used to calculate the rates in Table 2 show that the number of apprenticeship completions in 1995 was 17,075, increasing to 24,495 in 2007-an increase of about 43.5%.

^5.

Authors' calculations based on CANSIM Tables 477-0013 and 477-0014.

^6.

See www.ellischart.ca/h.4m.2@-eng.jsp (accessed 1 April 2010).

^7.

Boothby and Drewes (2006) estimate the weekly earnings premium for 25-to-34-year-old males with trades (and a high school diploma) to be about 15 percentage points higher than those with only a high school diploma in 2000. For females, the comparable estimate is a statistically insignificant 4.5 percentage points. However, Boothby and Drewes are unable to compare those who completed trades with those who did not.

^8.

Multinomial logit models were used at first, but Hausman tests rejected the "independence of irrelevant alternatives" (IIA) assumption in a number of cases. Despite the higher computational costs of obtaining marginal effects from multinomial probit models compared to multinomial logit models, this study uses the former. In practice, however, the results from the multinomial logit models were similar to those presented below.

^9.

A fourth choice is also theoretically possible: individuals can switch from one trade to another. Since the data are specific to the trade in which the apprentice is registered in the 2002-2004 period, switchers are not observed.

^10.

Due to different apprenticeship programs in different provinces, the error terms of individuals within provinces could be correlated. As such clustering within provinces is controlled for in all estimates.

^11.

Other data were considered as well. The Youth in Transition Survey (YITS) is very rich in family background, school experience, and aptitude variables, but it is difficult to identify those in apprenticeship programs. The 2006 Census of Population did ask specific questions regarding apprenticeship training and completion, and has a large sample size for analysis. Unfortunately, it lacks the richness of background variables which have been shown to be important controls in the PSE literature addressing college and university choice. The Registered Apprenticeship Information System (RAIS) is useful for the fact that it contains administrative-not survey-data and therefore is likely to have fewer measurement errors. However, the data available through the RAIS have limited background variables.

^12.

A limitation of these data is that they include only long-term continuers, defined as those who began their programs before 2000 and who had not completed their certification by the end of the survey period in 2004. Short-term continuers were not in the scope of the survey. Statistics Canada randomly selected the survey respondents from the administrative data lists provided by the provincial and territorial apprenticeship authorities. Some of these lists may not have been up-to-date; consequently, a number of short-term continuers were contacted and interviewed by Statistics Canada. These individuals are also included in the analysis. As with any survey data, there is the possibility that there exists non-random error in questionnaire responses. See Laporte and Mueller (2010) for a brief discussion of this issue with respect to the NAS data used here.

^13.

Including those who started their apprenticeship program at ages 14 and 15 did not change the results.

^14.

Some 63% of those who discontinued a program as of 2004 had returned to an apprenticeship program by 2007 (Ménard et al. 2008). This result suggests that one-time dropout rates should not be taken to imply discontinuation in the long-term. These results are similar to those obtained by Finnie and Qiu (2008), who show a similar phenomenon occurring at universities and colleges.

^15.

It should be noted that this variable is coded to one (zero otherwise) for individuals who speak a different language at home than at the worksite, where the worksite is the most recent job held. This may or may not reflect the language most often spoken at the worksite during the apprenticeship period. Given the number of apprentices who complete their programs with one employer, coupled with the high probability of remaining with the same employer following completion, this seems like a reasonable assumption to make.

^16.

As mentioned above, multinomial logit (MNL) models were initially used, since they are computationally more efficient, but Hausman tests rejected the "independence of irrelevant alternatives" (IIA) assumption in a number of cases. Despite this, the results from the MNL models were very similar to the results presented here. In addition, the models were also estimated using the apprenticeship status during the survey frame (2002-2004). Reasonably similar results to those presented here were found. Various other model specifications were attempted. They are not reported here in the interest of parsimony, but all are in accord with the results presented here.

^17.

In Appendix Text table 1, the coefficient on male is significantly negative in the first specification but then becomes positive and significant at the 10% level in the second specification when major trade group controls are added. A separate regression (not shown), which excluded the hairstylist-esthetician trade group, also yielded a positive coefficient on the male variables, again significant at 10%.

^18.

In the NAS, North American Indian, Métis and Inuit are grouped together under the same question and as a result the term Aboriginal has been used in this paper.

^19.

Variables for having an immigrant mother and/or an immigrant father were also included as variables in the model. The rationale for this was that the NAS contains no information on parental educational background and that many immigrant groups (e.g., Eastern Europeans) are heavily involved in the trades. Given the heritability of education in general, this variable is included in order to pick up this effect. The results are generally small and/or statistically insignificant. See Appendix Text table 1 for detailed results.

^20.

To see whether there were differences between Québec and the rest of Canada, two separate multinomial probit models were estimated, one with Québec and the other without Québec, but limiting the sample to only those in construction trades (not reported here). This was done, since the non-construction trade groups in Québec were either underreported or not reported in the NAS. The results between the two models were consistent with the main results presented here. An interesting difference was that the unemployment rate in both estimates was positively and statistically related to completion behaviour. Thus, the probability of completion could be positively influenced by the regional unemployment rate in the construction trades, whereas this cannot be said for the main estimates, which include all trades but exclude Québec (see Chart 9).

^21.

It is worthwhile to note that the inclusion of trade groups changes the coefficient on male completion from a highly significant -10.5 percentage points to a positive 5.1 percentage points, significant at the 10% level. Compare Models 1 and 2 in Appendix Text table 1.

^22.

This is defined for every respondent as the annual unemployment rate in the last year of his or her apprenticeship program by economic region (according to each person's postal code).

^23.

When estimating these models using the apprenticeship status over the 2002-2004 frame, there was no significant relationship between any of the three states and the unemployment rate. Given the nature of the 2002-2004 data, the average unemployment rate from 2002-2004 was used, and not the unemployment rate at the time of program completion for discontinuers and completers as has been done here.

^24.

Arguably, this could be the result of "streaming" into these programs amongst those who may not be academically gifted. To address this, the YAP variable was regressed on high school grades (not reported); no evidence of streaming was found. In fact the opposite was found, as participation in these programs increased in grades. It is quite possible, however, that high school grades are endogenous to the simple model if the grades as reported were tallied after the student moved into the YAP and improved his or her grades in the new program, thus biasing the results in the simple regression. There is no way of addressing this potential endogeneity in these data.

^25.

Unfortunately, the NAS does not ask a question regarding the language most often spoken during the apprenticeship program; this language may be different (especially in the case of completers and discontinuers) from the language currently spoken on the job. See footnote 15.