4 An accounting framework for degree-holder growth

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The goal of this paper is to identify the sources of degree-holder growth for a given age cohort within a geographic unit. From the perspective of a city or region, there are three sources of degree holders: net migration from other parts of Canada; net international migration; and, the 'graduation' ofindividuals from non-degree- to degree-holder status within the resident population or, put more succinctly, in situ growth. To identify the relative contribution of these three sources to degree-holder growth, we impose the counterfactual that no degree holders were added to the age cohort over the previous five years; that is, the number of degree holders in year t was the same as that in year t -5. This implies the following: first, no-one migrated—nationally or internationally—into or out of the geographic unit that had, or obtained, a degree over the ensuing five years; second, no-one who remained in the same location obtained a degree.

Our goal is to account for the difference between the actual and counterfactual level of degree holders across locations. This can be accomplished via two related steps. First, we impose the counterfactual that there was no movement of degree holders, and those that obtained degrees from 1996 to 2001, in or out of the geographic unit. This entails eliminating both any form of migration within Canada and any form ofinternational movement of degree holders. For time t , where t = 2001, the actual number of degree holders in age cohort c present in location j is given by:

where M is the number of migrants from all other locations i to j ( j ∈ Canada), I is the number of immigrants to j from outside of Canada and C is the number of degree holders in j that resided in the same location five years previous. The counterfactual entails sending everyone who left j back to j :

where the tilde indicates a counterfactual level of degree-holder employment and E is the number of degree holders that emigrated from j . Subtracting (1.2) from (1.1), allows us to define the contributions of net internal migration and international migration to degree holder growth:

In the second step, we impose the additional counterfactual that all persons in age cohort c in j did not obtain a degree; that is, the number of degree holders is the same as the five years previous, D^c_jt−5 . Subtracting D^c_jt−5 from (1.2) provides us with a measure of the growth of degree holders that results from the degree attainment:

Since (1.3) plus (1.4) equal D ^c_jt − D^c   _jt−5 , we can define the change in the level of degree holders for a given age cohort between periods as:

The first term of Equation (1.5) accounts for the contribution of net internal migration to the growth of degree holders. The second term measures the effect of net international migration in a similar fashion to the first term. The third and final term measures the influence of in situ growth of degree holders; that is, it captures the effect of those persons that obtained degrees over five years, regardless of whether they remained in or left location j . In total, (1.5) provides us with a means to account for the growth of degree holders within an age cohort, and to compare this growth across geographic classes.

The data required to calculate the relative contributions of net internal migration, net international migration and in situ growth to changes in the degree share of age cohorts are largely derived from the Censuses of1996 and 2001. These censuses provide information on the location and educational attainment of individuals. Hence, we can identify university-degree holders (hereafter referred to only as 'degree holders') in 2001 and 1996, and their location.

The 2001 Census also provides information on the location of individuals in 2001 and their location five years previous, allowing for the measurement of the migration of degree holders from 1996 to 2001. ³ From this it is possible to ascertain the census metropolitan area (CMA), census agglomeration (CA), and the province of the individual five years before. Hence, we can identify whether someone migrated to or from a rural area of a province, but little else. ⁴ In total, we can identify those degree holders that migrated in and out of CMAs, CAs and rural parts of each province. The territories are treated as a whole, with the exception of the CAs of Yellowknife and Whitehorse.

What we cannot measure from these census data are the number of emigrants with degrees. Statistics Canada, however, does provide estimates of the number of emigrants by year, age and location. ⁵ For our purposes, there are two limitations to these data. The first limitation is that the number of degree-holder emigrants is not estimated. To address this limitation, we assume the share of degree-holder emigrants matches that of their corresponding age group and geographic location among the general population in 2001. This is a strong assumption, but we make it with the knowledge that the rate of emigration is relatively low and so any error introduced will have little influence on our overall findings.

The second limitation is that the number of emigrants is tabulated by CMA and province only. Hence, we do not have estimates for CAs or rural areas. To provide estimates for these geographies, we use their provincial population shares to allocate non-CMA provincial emigrants. Since the magnitude of these non-CMA provincial residuals of emigrants is small, we feel that the error in calculating the size of the non-CMA sub-sets will not be of major consequence.

3. These migratory flows will include those persons that had obtained a degree prior to 1996 and those that obtained a degree between 1996 and 2001.

4 . We do know from the census whether a person resided in a rural census subdivision that had strong, moderate, weak or no commuting relationships with census metropolitan areas and census agglomerations, but ignore this distinction for this paper.

5 . Statistics Canada, Demography Division.