88 1.6
0
) 86 15 87 cc .i 89 90 78 84 1.2 83 80 1 82 14 10 12 16 6 8 Unemployment Rate (%) S o u rc e :L F S a n d E m p lo y m e n t G a z e tte 133measuring net gain or loss in utility is private information. Nevertheless when migration is observed the econometrician can infer there is a net gain in utility.
Assuming the probability of changing regions is appropriately described by a logistic distribution, the probability of individual migration is given by:
P(/,, = l) = P ( / „ * > 0 )
= />[£,([/,
— ^(Y t ^ i t ' ^ ^ i t ^ [5.4.1]
= P(e,, > - y ; z , )
= A (Y / Z ,)where A is the cumulative logistic distribution function^^.
Given these probabilities the likelihood function for observed regional mobility of a group of individuals can be written as:
I= \ 1=0
= n A(y, ' z„ ) n [1 -
/ 4 )]
[5.4.2]
/ = ! [=0
Maximising this hkelihood produces consistent and efficient estimates of parameters of the migration model provided that certain conditions are satisfied. However we suspect migration and the right hand side variable Z„ is simultaneously determined. This implies that the MLE estimates will no longer be consistent^. In the next section we discuss the nature and solutions to this problem.
65...=. A6.. exp(Y,'Z,,)
^^When Z„ is endogenous the score function (the first order conditions for maximising the log likelihood) converges to a non-zero population mean which makes MLE asymptotically biased.
5.4.1 Housing Tenure
Change of region is always accompanied by a change of home. Buying and selling dwellings can make regional migration for owner occupiers financially expensive. The system of public housing (also referred to as council or local authority housing) reserves a small number of properties for migrants but does not guarantee another council property. Such uncertain re-entry and lower rents than the private sector make it riskier for council tenants to change regions. Hughes and McCormick (1987) explain the tenure-migration linkage may be simultaneous because migration plans may influence the tenure choice prior to migration. But the existence of rationing and financial constraints may make this link relevant only for a few households so treating tenure as exogenous is innocuous. They also discuss the possibility that council migrants may be a self selected group. But since they find council tenants 60% more likely to move house within the same standard region than owner-occupiers they refute the possibility that council tenants have characteristics that make them less likely to move. However Bover et al (1989) express some doubt regarding the reliability of results such as these which are based on a small number of observations.
In this paper, it is argued, council tenants migrate less, not only because they lose their right to immediate occupancy of a council dwelling, but because, individuals who end up in public housing have unobservable characteristics that deter migration. In that sense it is similar to the self selection mentioned above but is strengthened on the basis that recent changes in housing policy has transformed council accommodation into housing of last resort^^; the better o ff moved out and the worse o ff moved in. For example, the ‘Right to Buy’ Act (1980) gave secured tenants the right to become owners of the property they occupied and, the Housing and Homelessness Act (1977) obhged local authorities to house individuals on priority needs (low income, homeless, single mothers, a young couple with a new baby). For these reasons, heads of household who remain council tenants will have httle bargaining power and fewer employment prospects. The presence of
such unobservables (in a potential migrant) may dampen expected utility in period (t+1) reducing the possibility that these individuals will satisfy the migration pre-condition (7„*>0).
If as we have argued, a negative correlation is present between the error term of the migration equation (unobservable characteristics which influence migration) and the type of housing tenure, treating housing as exogenous will result in a simultaneity bias of the housing tenure coefficient. Correct estimation of the migration equation requires an instrumental variable strategy, where instruments for the council, private and owner occupied properties can be found.
The model we estimate has three steps. Initially two simple logits, one for council housing and one for private housing are estimated using GHS data. In the second step, the coefficients of the GHS housing estimates together with the right hand side variables from LFS are used to impute the probability that each individual is a council tenant and the probability that the individual is a private tenant. In the final step, these two predicted probabilities are used together with other exogenous factors to fit an equation which explains migration behaviour^^.
Step 1: Logits for the probabilitv of housing type in GHS.
The probability of being a council tenant as opposed to a private tenant or an owner occupier depend on the value of the latent variable C„*.
P(council=l)=P(C„* >0) [5.4.3]
Similarly the probability of being a private renter as opposed to any other household type is determined by the value of the latent variable P„*.
P(private=l)=P(P„*>0) [5.4.4]
Assuming that these probabilities can be described by a logistic distribution the probability of living in a council home and a private home is given by the following equations
^*The method can be thought of as a variation of two stage least squares where ordinary least squares is substituted by maximum likelihood estimation.
C,-,* = a f , ^ X , î + a î X * J
where Xj is the vector of exogenous circumstances included in the migration model and X2 a vector of instruments excluded from the migration model. The first housing equation measures the probability of being a council tenant instead of an owner occupier or a private tenant. The second measures the probability of being a private tenant instead of an owner occupier of a council tenant.
Step 2: Imputing housing information into LFS.