The foundation for the study is a spatial interaction model as outlined by Alonso (1978). This model formulates migration flows as a function of relative attractiveness of origin and destination areas, and of frictions between areas. The flow from area i to area j is modelled as:
Mij(t) = c(t) Oi(t) Dj(t) Fij(t)
where Mij(t) is the migration flow from i to j c(t) is a constant
Oi(t) is the total forces 'pushing' people out of region i Dj(t) is the total force 'pulling' people into region j Fij(t) is the friction affecting flows between i and j
In the simplest gravity model, Oi and Dj are replaced by the populations of areas i and j respectively (each with an estimated exponent), and the friction term is replaced by a measure of the distance between i and j (also with an estimated exponent). See Nijkamp and Poot (1987) for a fuller discussion of the components of the spatial interaction model.
One of the main criticisms of such models is the lack of an explicit behavioural foundation that would justify the functional form used.96 While accepting that criticism, for our purposes, we suggest relying on a simple gravity relationship to capture the strong empirical patterns that are known to exist between population size, distance, and migration flows.
Our main interest is to estimate the relationship between migration and labour market conditions. We therefore suggest augmenting the basic model by adding appropriate measures of the relative attractiveness of local labour markets that are more closely linked to behavioural factors. Other measures could be added capturing factors that
96
Some progress has been made in developing microfoundations for gravity models in the context of international trade (Anderson and van Wincoop (2001) and Deardorff (1998)), although Deardorff (1998) has pointed out that a gravity equation is derivable from any plausible model of trade.
are suggested by theory and that could bias our estimates of labour market impacts if they were omitted.
The general form of the estimating equationwould be97:
(
1 2 3)
3 2 1 α α β β β α ij j i ij j i ijcP
P
D
X
X
F
M
=
where Pi and Pj are populations of areas i and j respectively Dij is the distance (or travel time) between i and j
Xi and Xj are other measures of the attractiveness of areas i and j Fij contains other measures of friction of flows between i and j.
Labour market measures
Measures of relative labour market attractiveness could include:
! relative employment rates: employment/working age population, or employment/labour force (depending on whether the employment chances of discouraged workers and non-participants are relevant for the migration decision) ! relative employment growth rate;
! relative wage rate (measured as average or median)
All relative measures are to be measured as deviations from national average so as to capture relative attractiveness98
Other measures of area relative attractiveness
In our discussion of key question one, we emphasised the potential importance of permanent differences in the attractiveness of an area. These could arise due to the presence of amenities, sustained differences in cost of living, etc. Where direct measures of environment, climate, infrastructure, etc. are available these can be included as covariates. Otherwise, location-specific attractiveness can be accommodated by methods such as fixed effects modelling.99
Where available, a range of other measures of attractiveness can be included, such as ! fiscal measures (net public provision of goods and services to an area);
! diversity or concentration measures (e.g. a broad based industrial structure may be attractive as it allows some 'insurance' by pooling industry-specific risks (see Maré and Timmins (2000)).
! neighbourhood measures: If using spatially coded data, it is possible to derive measures of characteristics of areas surrounding a particular location, which may be relevant for migration decisions (see Kerr, Maré et al. (2001)).
Composition differences
Another issue emphasised in the discussion of key question one was the importance of allowing for differences in demographic or employment composition. One of the costs of using area-level data rather than individual data is that the ability to control for inter- group differences in migration rates is limited. To the extent that these are also
97
For larger geographical areas, the equation can be estimated in log form by linear regression. For smaller geographical areas, such as area units, some areas will have zero inflows or outflows, so the log transformation is not appropriate, and some form of nonlinear estimation (eg: maximum likelihood) is needed.
98
This would not be appropriate if we wished to understand international migration flows as well, as it ignores the relative attractiveness of New Zealand compared with other countries. See below for a brief discussion of the treatment of international migration
99
See Mátyás (1997), Mátyás (1998), and Eggers (2000) for a discussion of estimating gravity models with panel data. See also Isard (1998) and Sen and Smith (1995) for a more complete discussion of gravity model specification issues.
correlated with labour market conditions, estimates of the relationship between migration and labour markets could be biased.
At a minimum, measures of demographic composition along key dimensions such as age, gender, marital status, ethnicity, home ownership, industry mix should be included as covariates. As with the attractiveness measures, these should be measured as deviations from national means.
Measures of Friction
As noted above, the most common measure of migration friction is distance between locations. We consider that travel time is superior to linear (crow-flight) distance. When using area-level data, each area must be assigned a specific location. We consider population centroids as the most appropriate measure for migration modelling. Indicators of physical barriers between any pair of locations, such as Cook Strait or the Southern Alps can be included in order to test whether they represent any additional friction.
When looking at links between migration and labour markets, it is plausible to consider more general forms of 'distance' or dissimilarity between locations. For instance, migration may be stronger between areas that have similar occupational mixes, age structure, ethnic mix, or industrial composition. Conley and Topa (2000) argue that such measures capture aspects of social and information networks. Some may also reflect the importance of industry or occupation-specific human capital.
A related concept that is common in the internal migration literature is that of the "well- worn-path". Migration flows will be stronger between two areas where there has been significant past migration. Sometimes, lagged migration flows are included to reflect this factor. An alternative that we suggest is to express the sum of inter-area flows for a given pair of areas as a proportion of the sum of their populations. This approximates the proportion of the two areas' populations that have (recently) lived in both regions.
Administrative boundaries have also been included as possible sources friction. In the context of a New Zealand internal migration study, regional council or territorial local authority boundaries can be used where the unit of observation is an area unit.