of the unemployment equation (and it is also the case of the public housing variable in the
neighborhood choice equation), it amounts to a mixed model, which is consistent only if it has
the form of a triangular system (Maddala, 1983). Therefore, the observed variable of unemploy-
ment can not be introduced in the other two equations of neighborhood type and public housing
accommodation. Nonetheless, we may think that residential demand is influenced by the latent
variable determining unemployment more than by the observed variable itself. Consequently, all
the variables determining the latent variable of unemployment are included in the neighborhood
and public housing equations. Moreover, as the simultaneous probit model enables us to deal
with correlation between unobservables, the effect of unobservables determining both unemploy-
ment and residential choices are taken into account. Neighborhood type is also explained by
spouse’s educational level, that gives further information on permanent income of the household,
and dummies for the number of children in the household, that determine housing floor space
need and the propensity to settle in neighborhoods where housing rents are low. As a large
share of deprived neighborhoods inhabitants are public housing tenants, public housing is also
supposed to determine the probability to live in a deprived neighborhood.
As far as the public housing equation is concerned, one may think that neighborhood
influences public housing choice: households that do not desire to locate in a deprived neigh-
borhood might be deterred from applying to the public sector due to the location of public
housing units. This means that the latent variable determining neighborhood choice may in-
fluence tenure choice and implies introducing all exogeneous variables influencing neighborhood
choice in the public housing equation. Being housed in the public housing sector (which reflects
both that the individual applied for and obtained a public housing unit) is then explained by
the same variables as the neighborhood choice, with the addition of the spouse’s age, because
young households are given preferential attribution of public housing units. The complete list
of variables and their descriptive statistics are given in Table 1.
In summary, the observed variables y1 , y2 and y3 referring respectively to unemployment,
location in a disadvantaged neighborhood and public housing accommodation are defined by:
1 if yî > 0,
(2.1)
(2.2)
(2.3)
y1 =
I 0 otherwise
1 if y2î > 0,
y2 =
I 0 otherwise
1 if y3î > 0,
y3 =
I 0 otherwise