The B.E.Journal of Economic Analysis Policy,Vol.7 [2007],Iss.I (Advances),Art.62 Equation (1)relates the responses to the four questions regarding further immigration in the 1 x 4 vector y;to the three "latent factors"fi which we have described above (labour market,welfare,and cultural/racial concerns), conditional on individual and contextual information Xi.Consequently,fi is a 1 x 3 vector,with coefficients in the 3 x 4 matrix A.As we only observe discrete responses to questions regarding further immigration,y;is a vector of latent responses.A is a k x 4 matrix of conditional responses of attitudes to k other observed characteristics Xi(such as age,education etc.).The term ui is an error term,and we assume that ui~N(0,u).The parameters in the matrix A are the main parameters of interest;they measure the magnitude of association between each of the three concerns we consider,and attitudes to further immigration. Equation(2)relates the latent factors to the regressors Xi,where B is a k x3 matrix of coefficients,and vi~N(0,)Finally,equation (3)relates the set of responses that relate to each of the three factors,z,to the latent factors fi and observed characteristics Xi.In our case,we observe 10 responses that "reveal"the fi:four for labour market concerns,three for welfare concerns, and three for racial and cultural concerns.Accordingly,2;is a 1 x 10 vector, M is a 3 x 10 matrix of coefficients,and C is a k x 10 matrix of conditional responses to Xi.Again,as only discrete responses are observed,2 is a vector of latent responses.We assume that wi~N(0,) We further assume that ui and wi are uncorrelated with Xi and fi,which implies that they are also uncorrelated with vi.Therefore,Elu==0 andE[w=∑uw=0. Consider now the reduced form equations,which are obtained by substi- tuting (2)in (1)and (3): Xi(BA+A)+ui+viA=XiT1+ei, (4 and =Xi(BM+C)+wi+viM=XiT2+e2i, (5) where i=[eile2i]'~N(0,>)The matrix ∑u+A∑，A'∑uw+M∑，' 212 w+A∑，M'∑w+M∑M' (6) is the (4+10)x(4+10)variance-covariance matrix of the reduced form residuals and∑e denotes E(uw). http://www.bepress.com/bejeap/vol7/iss1/art62 6Equation (1) relates the responses to the four questions regarding further immigration in the 1 4 vector y i to the three ìlatent factorsî fi which we have described above (labour market, welfare, and cultural/racial concerns), conditional on individual and contextual information Xi . Consequently, fi is a 1 3 vector, with coe¢ cients in the 3 4 matrix . As we only observe discrete responses to questions regarding further immigration, y i is a vector of latent responses. A is a k 4 matrix of conditional responses of attitudes to k other observed characteristics Xi (such as age, education etc.). The term ui is an error term, and we assume that ui  N(0; u). The parameters in the matrix are the main parameters of interest; they measure the magnitude of association between each of the three concerns we consider, and attitudes to further immigration. Equation (2) relates the latent factors to the regressors Xi , where B is a k3 matrix of coe¢ cients, and vi  N(0; v). Finally, equation (3) relates the set of responses that relate to each of the three factors, z i , to the latent factors fi and observed characteristics Xi . In our case, we observe 10 responses that ìrevealî the fi : four for labour market concerns, three for welfare concerns, and three for racial and cultural concerns. Accordingly, z i is a 1 10 vector, M is a 3 10 matrix of coe¢ cients, and C is a k 10 matrix of conditional responses to Xi . Again, as only discrete responses are observed, z i is a vector of latent responses. We assume that wi  N(0; w): We further assume that ui and wi are uncorrelated with Xi and fi , which implies that they are also uncorrelated with vi . Therefore, E[uiv 0 i ] = uv = 0 and E[wiv 0 i ] = wv = 0. Consider now the reduced form equations, which are obtained by substi￾tuting (2) in (1) and (3): y i = Xi(B + A) + ui + vi = Xi￾1 + 1i ; (4) and z i = Xi(BM + C) + wi + vi M = Xi￾2 + 2i ; (5) where i = [1i j2i ] 0  N(0; ). The matrix  = 0 @ u + v 0 uw + M v 0  0 uw + v M0 w + M v M0 1 A  0 @ 11 12  0 12 22 1 A (6) is the (4+10)(4+10) variance-covariance matrix of the reduced form residuals and uw denotes E(uiw 0 i ). 6 The B.E. Journal of Economic Analysis & Policy, Vol. 7 [2007], Iss. 1 (Advances), Art. 62 http://www.bepress.com/bejeap/vol7/iss1/art62