Dustmann and Preston:Racial and Economic Factors in Attitudes to Immigration 2 Separating Factors in Attitudes to Immigra- tion 2.1 Econometric Specification The idea of our empirical approach is as follows.The variable we wish to explain is the respondent's attitude to further immigration.In our data,this question is asked four times,distinguishing between four different origin re- gions (India/Pakistan,the West Indies,Europe,and Australia/New Zealand). We relate these responses to three(unobserved)channels (or factors)through which attitudes may be formed:labour market concerns,welfare concerns, and cultural or racial prejudice.We identify three sets of questions in the BSA regarding issues which are each strongly related to one or other of these channels.Questions regarding labour market security include questions on the fear of job loss,the ease of finding a job and expected future wage paths. Questions indicating welfare concerns include a question on adequacy of ben- efit levels,perception of recipients'needs,and willingness to pay for increased public social spending.Questions indicating racial or cultural attitudes in- clude attitudes towards inter-ethnic marriage,having a minority boss,and self admitted prejudice against minorities.We report the wording of the questions in Appendix D. We use responses to these sets of questions to isolate a common element for each of the three factors.One way of doing this would be to take some average of each of the three sets of responses for each respondent,and to regress,in a second step,the overall response to the immigration question on the new variables obtained in this way.This is conceptually similar to our approach, which can be thought of as weighting and normalising the single questions when combining them into a single factor.The approach we follow makes more efficient use of the data.Further,we adopt a normalisation that allows comparison of magnitudes of coefficients across the different responses. We now explain our procedure in more detail.Our model consists of three equations: yi=fiA XiA +ui, (1) fi=XiB+vi, (2) z=fiM+XiC+wi. (3) Published by The Berkeley Electronic Press,2007
2 Separating Factors in Attitudes to Immigration 2.1 Econometric SpeciÖcation The idea of our empirical approach is as follows. The variable we wish to explain is the respondentís attitude to further immigration. In our data, this question is asked four times, distinguishing between four di§erent origin regions (India/Pakistan, the West Indies, Europe, and Australia/New Zealand). We relate these responses to three (unobserved) channels (or factors) through which attitudes may be formed: labour market concerns, welfare concerns, and cultural or racial prejudice. We identify three sets of questions in the BSA regarding issues which are each strongly related to one or other of these channels. Questions regarding labour market security include questions on the fear of job loss, the ease of Önding a job and expected future wage paths. Questions indicating welfare concerns include a question on adequacy of beneÖt levels, perception of recipientsíneeds, and willingness to pay for increased public social spending. Questions indicating racial or cultural attitudes include attitudes towards inter-ethnic marriage, having a minority boss, and self admitted prejudice against minorities. We report the wording of the questions in Appendix D. We use responses to these sets of questions to isolate a common element for each of the three factors. One way of doing this would be to take some average of each of the three sets of responses for each respondent, and to regress, in a second step, the overall response to the immigration question on the new variables obtained in this way. This is conceptually similar to our approach, which can be thought of as weighting and normalising the single questions when combining them into a single factor. The approach we follow makes more e¢ cient use of the data. Further, we adopt a normalisation that allows comparison of magnitudes of coe¢ cients across the di§erent responses. We now explain our procedure in more detail. Our model consists of three equations: y i = fi + Xi A + ui ; (1) fi = Xi B + vi ; (2) z i = fi M + Xi C + wi : (3) 5 Dustmann and Preston: Racial and Economic Factors in Attitudes to Immigration Published by The Berkeley Electronic Press, 2007
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 6
Equation (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 substituting (2) in (1) and (3): y i = Xi(B + A) + ui + vi = Xi1 + 1i ; (4) and z i = Xi(BM + C) + wi + vi M = Xi2 + 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
Dustmann and Preston:Racial and Economic Factors in Attitudes to Immigration Our estimation strategy now proceeds in three stages.In the first stage, we estimate the reduced form coefficient matrix I =TT2]'.We do that by estimating the coefficients of each equation in (4)and (5)(corresponding to the rows of r)separately by independent (ordered)probits.Due to the discrete nature of the dependent variables,we can only estimate their ratios to the standard deviations of the associated error components. In the second stage we obtain the parameters in X.Again,a normali- sation assumption is required.We adopt the identifying normalisation that the diagonal elements in X and in X are such as to make the diagonal ele- ments of e equal to unity.To estimate e,we take each pairing of questions successively,and estimate the corresponding off-diagonal component of e by bivariate maximum likelihood.We fix the coefficients of the two equations concerned at the values in I estimated in the previous stage.4 Finally,in the third step we estimate the parameters in M,A and X using ninimum distance estimation and the restrictions∑22=∑e+M∑，M'and 12=+MA'.To do so,we make the following assumptions.First,we assume that each of our indicator questions in z*is indicative of one and only one factor.For instance,the three questions on the labour market are assumed to be affected only through the labour market channel,the three questions on welfare concerns only through the welfare channel,and so on.This means that we assume that MM'is a block diagonal matrix,with only one non-zero element in each row of M.Second,we assume that all correlation between responses to these questions (conditional on the regressors Xi)is accounted for by the factor structure,which implies diagonality of the matrix.Notice that we allow for correlation between the factors,since is not required to be diagonal.Finally,we set the diagonal elements of o to unity,which is simply a normalising assumption. Given these assumptions,there is sufficient information in >22 from the con- ditional correlations between responses within blocks to identify all elements of M.5 Having identified M,the off-diagonal elements of Xo are identified without 4Consider for instance the responses to the first two immigration questions,with the latent two equation model being yii Xi71+e1i and y2=Xiy2+e2i.We estimate the covariance Cov(eli,2i)using a bivariate probit likelihood,where we fix Y1 and Y2 at the estimates obtained in the first stage,Y and 72. 5Remembering the particular structure of MEM',suppose that the ith diagonal block has gi elements.Then there are gi(qi-1)/2 off-diagonal elements in the corresponding block of S22 from which to identify them.This is sufficient if gi 3,which is so for each block in our case.This is not to say that the condition is necessary since there is also identifying information in the elements of off-diagonal blocks. Published by The Berkeley Electronic Press,2007 7
Our estimation strategy now proceeds in three stages. In the Örst stage, we estimate the reduced form coe¢ cient matrix = [1j2] 0 . We do that by estimating the coe¢ cients of each equation in (4) and (5) (corresponding to the rows of ) separately by independent (ordered) probits. Due to the discrete nature of the dependent variables, we can only estimate their ratios to the standard deviations of the associated error components. In the second stage we obtain the parameters in . Again, a normalisation assumption is required. We adopt the identifying normalisation that the diagonal elements in u and in w are such as to make the diagonal elements of equal to unity. To estimate , we take each pairing of questions successively, and estimate the corresponding o§-diagonal component of by bivariate maximum likelihood. We Öx the coe¢ cients of the two equations concerned at the values in estimated in the previous stage.4 Finally, in the third step we estimate the parameters in M, and v using minimum distance estimation and the restrictions 22 = w + M v M0 and 12 = uw +M v 0 . To do so, we make the following assumptions. First, we assume that each of our indicator questions in z is indicative of one and only one factor. For instance, the three questions on the labour market are assumed to be a§ected only through the labour market channel, the three questions on welfare concerns only through the welfare channel, and so on. This means that we assume that MM0 is a block diagonal matrix, with only one non-zero element in each row of M. Second, we assume that all correlation between responses to these questions (conditional on the regressors Xi) is accounted for by the factor structure, which implies diagonality of the w matrix. Notice that we allow for correlation between the factors, since v is not required to be diagonal. Finally, we set the diagonal elements of v to unity, which is simply a normalising assumption. Given these assumptions, there is su¢ cient information in 22 from the conditional correlations between responses within blocks to identify all elements of M. 5 Having identiÖed M, the o§-diagonal elements of v are identiÖed without 4Consider for instance the responses to the Örst two immigration questions, with the latent two equation model being y 1i = Xi 1 + 1i and y 2i = Xi 2 + 2i . We estimate the covariance Cov(1i ; 2i) using a bivariate probit likelihood, where we Öx 1 and 2 at the estimates obtained in the Örst stage, ^1 and ^2 . 5Remembering the particular structure of MM0 , suppose that the ith diagonal block has qi elements. Then there are qi (qi1)=2 o§-diagonal elements in the corresponding block of 22 from which to identify them. This is su¢ cient if qi 3, which is so for each block in our case. This is not to say that the condition is necessary since there is also identifying information in the elements of o§-diagonal blocks. 7 Dustmann and Preston: Racial and Economic Factors in Attitudes to Immigration Published by The Berkeley Electronic Press, 2007
The B.E.Journal of Economic Analysis Policy,Vol.7 [2007],Iss.I (Advances),Art.62 further restriction from the remaining elements of X22,that is to say from the correlations between elements in different blocks.Since all conditional correlation between responses in different blocks is assumed to be driven solely by the correlation between factors,considerable overidentifying restrictions are involved at this point.We report tests of these restrictions. Identification of A comes from the elements of 12.We assume that the correlation between responses to the immigration questions y*and the indica- tor questions 2*is accounted for by the factors f,conditional on observables X.This implies that∑uw=0 and therefore2=M∑，'.With M and∑w identified before,this is sufficient to identify A if p<g,which is to say that there are fewer factors than indicator questions.With p =3 and g =10,this is clearly the case in our application.To estimate the parameters in M,A and we impose in the third stage the restrictions on 2 and 22 by minimum distance. Computation of the variance-covariance matrix of the parameters is de- scribed in full in Appendix A.The estimation procedure outlined above does not guarantee positive semi-definiteness of the estimated asymptotic variance- covariance matrix for the parameter estimates,and we describe in the Appen- dix how we deal with that.6 Our main focus is the coefficients in A,and how they relate to each other in magnitude.Note that A dy/dfi and neither y nor fi,both being latent,have a unique natural scale of variation.However,the commonality of normalisation imposed here justifies comparability of coefficients within A.7 which is important for the interpretation of our results below.Given also the common form of the questions regarding immigration policy,it makes sense to compare the elements in A in terms of effects on probabilities,which is how we report them below.s The most critical assumption sustaining a causal interpretation of A is that u =0,which implies that E(y,)=E((f,),Xi).In other words,conditional on observables Xi,all association between y and z;should come through the three factors.This assumption would be violated if,for example,unobserved individual heterogeneity that affects labour market con- cerns is at the same time correlated with opposition to further immigration, conditional on Xi.Although we believe that much of the individual hetero- 6All programs are written by the authors in GAUSS and are available on request. 7That is to say,the residual variances along the diagonals of Ee and are each set to unity. sIn other words,we report (XiP)A,where we evaluate X at sample averages so that the values can be interpreted as the effect of a one standard deviation change in the relevant component of fi on the probability of hostility to immigration. http://www.bepress.com/bejeap/vol7/iss1/art62 8
further restriction from the remaining elements of 22, that is to say from the correlations between elements in di§erent blocks. Since all conditional correlation between responses in di§erent blocks is assumed to be driven solely by the correlation between factors, considerable overidentifying restrictions are involved at this point. We report tests of these restrictions. IdentiÖcation of comes from the elements of 12. We assume that the correlation between responses to the immigration questions y and the indicator questions z is accounted for by the factors f, conditional on observables X. This implies that uw = 0 and therefore 12 = M v 0 . With M and v identiÖed before, this is su¢ cient to identify if p q, which is to say that there are fewer factors than indicator questions. With p = 3 and q = 10, this is clearly the case in our application. To estimate the parameters in M, and v, we impose in the third stage the restrictions on 12 and 22 by minimum distance. Computation of the variance-covariance matrix of the parameters is described in full in Appendix A. The estimation procedure outlined above does not guarantee positive semi-deÖniteness of the estimated asymptotic variancecovariance matrix for the parameter estimates, and we describe in the Appendix how we deal with that.6 Our main focus is the coe¢ cients in , and how they relate to each other in magnitude. Note that = dy i =dfi and neither y i nor fi , both being latent, have a unique natural scale of variation. However, the commonality of normalisation imposed here justiÖes comparability of coe¢ cients within , 7 which is important for the interpretation of our results below. Given also the common form of the questions regarding immigration policy, it makes sense to compare the elements in in terms of e§ects on probabilities, which is how we report them below.8 The most critical assumption sustaining a causal interpretation of is that uw = 0, which implies that E(y i jz i ; Xi) = E(y i jE(fi jz i ; Xi); Xi). In other words, conditional on observables Xi , all association between y i and z i should come through the three factors. This assumption would be violated if, for example, unobserved individual heterogeneity that a§ects labour market concerns is at the same time correlated with opposition to further immigration, conditional on Xi . Although we believe that much of the individual hetero- 6All programs are written by the authors in GAUSS and are available on request. 7That is to say, the residual variances along the diagonals of and v are each set to unity. 8 In other words, we report (Xi), where we evaluate X at sample averages so that the values can be interpreted as the e§ect of a one standard deviation change in the relevant component of fi on the probability of hostility to immigration. 8 The B.E. Journal of Economic Analysis & Policy, Vol. 7 [2007], Iss. 1 (Advances), Art. 62 http://www.bepress.com/bejeap/vol7/iss1/art62
Dustmann and Preston:Racial and Economic Factors in Attitudes to Immigration geneity that is not already captured by the factors is likely to be captured by our observables Xi,we can not exclude this possibility and therefore prefer to refer to the estimated parameters as "associations"rather than "effects" The fact that none of the questions on which the identification of our factors is based refer specifically to further immigration can be regarded as reducing the potential for spurious correlation. 3 Background and Data 3.1 Immigrants in the UK According to the 2001 UK Census,the percentage of foreign-born individuals in the British population is 8.3 percent (or 4.9 million),almost twice as high as in 1951,when the corresponding number was 4.2 percent.Britain has always been a destination for intra-European immigrants,most notably for the Irish (Chance,1996).However,in the post-war period,Britain saw large numbers of immigrants arriving who were ethnically different from the predominantly white resident population. Immigration of Commonwealth citizens was most pronounced in the two decades after the war.While the early 1950s were characterised by migration from the Caribbean,in the late 1950s a growing number of immigrants ar- rived from the Indian subcontinent.Later immigrants arrived from Pakistan and Bangladesh.Labour market shortages in the period after the war led also to recruitment of European workers to fill certain labour market short- ages.These workers were predominantly from Southern Europe,but also from Poland.After the 1971 act,an increasing fraction of immigration was due to family unification,which remained for a time largely unrestricted.Favourable economic conditions in Europe prevented large migrations after 1971.Govern- mental response to the Ugandan Asian crisis of 1972 nevertheless led,despite the restrictive legislation adopted by then,to a renewed boost in the settle- ment of those of Asian origin.For further details on immigration to the UK. see Wheatley-Price and Hatton (2005)and Spencer (1997). The questions regarding immigrant origin asked in the BSA and which we consider in our analysis below,relate to individuals from three immigration areas:the West Indies,India and Pakistan,the area of the (then)European common market,and Australia/New Zealand.Over the period which we con- sider (1983-1990),immigrants from these four groups form about 63 percent of Throughout the paper,we refer to this source of immigration as "Asian",in line with wording typically used in the BSA. Published by The Berkeley Electronic Press,2007 9
geneity that is not already captured by the factors is likely to be captured by our observables Xi , we can not exclude this possibility and therefore prefer to refer to the estimated parameters as "associations" rather than "e§ects". The fact that none of the questions on which the identiÖcation of our factors is based refer speciÖcally to further immigration can be regarded as reducing the potential for spurious correlation. 3 Background and Data 3.1 Immigrants in the UK According to the 2001 UK Census, the percentage of foreign-born individuals in the British population is 8.3 percent (or 4.9 million), almost twice as high as in 1951, when the corresponding number was 4.2 percent. Britain has always been a destination for intra-European immigrants, most notably for the Irish (Chance, 1996). However, in the post-war period, Britain saw large numbers of immigrants arriving who were ethnically di§erent from the predominantly white resident population. Immigration of Commonwealth citizens was most pronounced in the two decades after the war. While the early 1950s were characterised by migration from the Caribbean, in the late 1950s a growing number of immigrants arrived from the Indian subcontinent. Later immigrants arrived from Pakistan and Bangladesh. Labour market shortages in the period after the war led also to recruitment of European workers to Öll certain labour market shortages. These workers were predominantly from Southern Europe, but also from Poland. After the 1971 act, an increasing fraction of immigration was due to family uniÖcation, which remained for a time largely unrestricted. Favourable economic conditions in Europe prevented large migrations after 1971. Governmental response to the Ugandan Asian crisis of 1972 nevertheless led, despite the restrictive legislation adopted by then, to a renewed boost in the settlement of those of Asian origin. For further details on immigration to the UK, see Wheatley-Price and Hatton (2005) and Spencer (1997). The questions regarding immigrant origin asked in the BSA and which we consider in our analysis below, relate to individuals from three immigration areas: the West Indies, India and Pakistan,9 the area of the (then) European common market, and Australia/New Zealand. Over the period which we consider (1983-1990), immigrants from these four groups form about 63 percent of 9Throughout the paper, we refer to this source of immigration as "Asian", in line with wording typically used in the BSA. 9 Dustmann and Preston: Racial and Economic Factors in Attitudes to Immigration Published by The Berkeley Electronic Press, 2007