Neighborhood Effects, Public Housing and Unemployment in France

where y∣, y⅛ and y₃ are latent variables influencing the probability of unemployment, the proba-
blity to live in a deprived area, and the probability to be renter in the public sector respectively.

The system of latent variables is as follows:

У1 = α1X1 + βy2 + γy3 + uι

< У2 = α2X2 + δy3 + U2

Уз = α3X3 + u3

where X1 is a vector of exogenous variables including a constant, individual’s age and its
square, nationality, diploma and previous occupation as well as the spouse’s nationality (each of
them being a set of dummy variables), X2 includes the same set of variables as X1, the spouse’s
diploma and dummies for the number of children and X₃ includes the same set of variables as
X2 and the age of the spouse. β and γ test for the influence on unemployment probability of
neighborhood type and public housing accommodation respectively.

As we assume that the sorting of households in deprived neighborhoods may be affected
by unobserved characteristics influencing simultaneously unemployment and residential choice,
the correlation terms between the residuals of the three probits (u1, u2 and u3) are all supposed
to be non-zero. The vector of residuals (u1, u2, u3) follows thus a normal trivariate law with zero
means and a covariance matrix that writes, after normalizations to 1 of the diagonal elements
as usual in probit models:

Such a system can be estimated by a maximum likelihood method. Endogeneity tests
amount to test the significance of the correlation coefficients of residuals between two equa-
tions.⁶ Note also that we use Huber adjusted standard errors, that is, we calculate a robust
variance matrix which accounts for the potential dependence of residuals within neighborhoods.
Indeed, the literature on neighborhood effects underlines the biases that stem from the possible
existence of common random shocks affecting all the individuals in a neighborhood. Our sample
having a large number of clusters and few individuals in each cluster, coefficients of cluster-level
variables are consistently estimated, but the variance matrix must be corrected for within-cluster
dependence (Wooldridge, 2003).

⁶Fabbri et al. (2004) show by means of a Monte-Carlo study that in a bivariate probit model, the likelihood
ratio test performs well for testing this significance.

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