LABOR MARKET COMPETITION AND INDIVIDUAL PREFERENCES OVER IMMIGRATION POLICY 139 (King et al.,2001;Schafer,1997;Little Rubin,1987; TABLE 1.-SUMMARY STATISTICS Rubin,1987).Multiple imputation makes a much weaker Variable 1992 1994 1996 assumption than does listwise deletion about the process Immigration Opinion 3.595 3.982 3.785 generating the missing data.Rather than assuming that the (1.027) (1.064) (0.982) unobserved data is missing completely at random,multiple Occupation Wage 0.512 0.574 0.601 imputation is consistent and gives correct uncertainty esti- (0.187) (0.227) (0.225) Education Years 12.923 13.153 13.328 mates if the data are missing randomly conditional on the (2.815) (2.637) (2.660) data included in the imputation procedures.The approach Gender 0.534 0.534 0.552 has several variations but always involves three main steps. (0.499) (0.499) (0.497) Age 45.755 46.264 47.544 First,some algorithm is used to impute values for the (17.711) (17.646) (17.416) missing data.In this step,m(m>1)"complete"data sets Black 0.129 0.115 0.122 are created consisting of all the observed data and imputa- (0.336 (0.319) (0.327) Hispanic 0.072 0.046 0.087 tions for the missing values.The second step simply in- (0.259) (0.209) (0.282) volves analyzing each of the m data sets using standard Immigrant 0.181 0.166 0.147 complete-data statistical methods.The final step combines (0.385) (0.371) (0.355) Party ID 3.701 3.916 3.673 the parameter estimates and variances from the m complete- (2.027) 2.102) (2.102) data analyses to form a single set of parameter estimates and Ideology 4.237 4.446 4.275 variances.Importantly,this step systematically accounts for (1.399) (1.348) (1.398) High Immigration MSA 0.235 0.227 0.215 variation across the m analyses due to missing data in (0.424) (0.419) (0.411) addition to ordinary sample variation. Number of observations 1795 The first step in our multiple-imputation procedures was 2485 1714 to create imputations in the missing data cells for all the Thesesmmary statisticsare multiple-imputaionsimates based on the ten imputed data setsfor each year.Each cell reports the variable mean and (in parenthesis)its standard deviation.Occipcrrlon Wige variables discussed in subsection IV A.We based our reports the actual weekly wage divided by 1000. imputations for the 1992,1994,and 1996 data on 36,28, and 26 variables selected,respectively,from each NES nonimputed information;they differ only in the imputations survey.These variables included all those used in our for missing data. analysis as well as additional information from each survey The second step in our multiple-imputation analysis was that we determined would be helpful in predicting the to run various ordered-probit models separately on each of missing data.10 Altogether,we imputed ten complete indi- the ten final data sets for each survey year.The last multiple- vidual-level data sets for each year.The exact imputation imputation step was to combine the ten sets of estimation algorithm we used is known by the acronym EMis because results for each specification to obtain a single set of to generate imputations it combines a well-known expecta- estimated parameter means and variances.The single set of tion-maximization missing-data algorithm with a round of estimated means is simply the arithmetic average of the ten importance sampling.King et al.(2001)provide a complete different estimation results.The single set of estimated explanation of the use of this algorithm for missing data variances is more complicated than a simple average be- problems.12 The final data sets for each year contain com- cause,as mentioned above,these variances account for both pleted observations equal to the actual number of individ- the ordinary within-sample variation and the between-sam- uals in each NES survey.Also,all data sets contain the same ple variation due to missing data.See King et al.(2001)and Schafer (1997)for a complete description of these vari- i0 For 1992,the variables included in the imputation model were ances. Immigration Opinion,Occupation Wage,Education Years,Gender,Age, Table 1 reports the summary statistics of our immigra- Black,Hispanic,Immigrant,Party ID,Ideology,High Immigration MSA. interactions of High Immigration MSA with skill measures,a continuous tion-opinion measure and explanatory variables calculated measure of percent immigrant in MSA/county of respondent,feeling by pooling together all ten of the imputed data sets for each thermometer scores for Hispanics and immigrants.family income,home year.The average value for Immigration Opinion was 3.60 ownership,union membership,retrospective evaluation of the national economy,retrospective evaluation of respondent's personal finances,three in 1992.3.98 in 1994,and 3.79 in 1996.The values reflect measures of respondent's tolerance,three responses to questions about the responses between "left the same as it is now"and "de- impact of Hispanic immigration on the United States,three responses to creased a little."13 questions about the impact of Asian immigration on the United States,the respondent's view of welfare restrictions for immigrants,three measures of the skill composition of immigrants in the respondent's geographical 13 For 1992,the exact breakdown of all responses to Immigration location,and a sample weighting variable.For 1994 and 1996,these same Opinion is as follows:58"increased a lot"(2.3%of the total sample,or variables,if available in the survey.were included.The variables for the 2.485):116 "increased a little"(4.7%).937 "left the same"(37.7%),552 imputation model were selected because they were included in the “decreased a little'”(22.2%),and505“decreased a lot'"(20.3%).In analysis models,were highly predictive of variables in the analysis model. addition,we imputed responses for the 87 people(3.5%)who responded or were highly predictive of the missingness in the data. "don't know/no answer"and the 230 people (9.3%)who were not asked The imputation procedures were implemented using Amelia:A Pro- the question because of survey design.(All results reported in the paper gram for Missing Data (Honaker et al.,1999). are robust to excluding these 230 observations from the analysis.)We also 12 In this analysis,the imputation model was multivariate normal with a note that the summary statistics in our data are similar to those obtained slight ridge prior. from the Current Population Survey(CPS).For example,in the 1992 CPS, This content downloaded from 202.120.14.193 on Mon,15 Feb 2016 10:04:26 UTC All use subject to JSTOR Terms and ConditionsLABOR MARKET COMPETITION AND INDIVIDUAL PREFERENCES OVER IMMIGRATION POLICY 139 (King et al., 2001; Schafer, 1997; Little & Rubin, 1987; Rubin, 1987). Multiple imputation makes a much weaker assumption than does listwise deletion about the process generating the missing data. Rather than assuming that the unobserved data is missing completely at random, multiple imputation is consistent and gives correct uncertainty esti￾mates if the data are missing randomly conditional on the data included in the imputation procedures. The approach has several variations but always involves three main steps. First, some algorithm is used to impute values for the missing data. In this step, m(m > 1) "complete" data sets are created consisting of all the observed data and imputa￾tions for the missing values. The second step simply in￾volves analyzing each of the m data sets using standard complete-data statistical methods. The final step combines the parameter estimates and variances from the m complete￾data analyses to form a single set of parameter estimates and variances. Importantly, this step systematically accounts for variation across the m analyses due to missing data in addition to ordinary sample variation. The first step in our multiple-imputation procedures was to create imputations in the missing data cells for all the variables discussed in subsection IV A. We based our imputations for the 1992, 1994, and 1996 data on 36, 28, and 26 variables selected, respectively, from each NES survey. These variables included all those used in our analysis as well as additional information from each survey that we determined would be helpful in predicting the missing data.10 Altogether, we imputed ten complete indi￾vidual-level data sets for each year.1' The exact imputation algorithm we used is known by the acronym EMis because to generate imputations it combines a well-known expecta￾tion-maximization missing-data algorithm with a round of importance sampling. King et al. (2001) provide a complete explanation of the use of this algorithm for missing data problems.12 The final data sets for each year contain com￾pleted observations equal to the actual number of individ￾uals in each NES survey. Also, all data sets contain the same nonimputed information; they differ only in the imputations for missing data. The second step in our multiple-imputation analysis was to run various ordered-probit models separately on each of the ten final data sets for each survey year. The last multiple￾imputation step was to combine the ten sets of estimation results for each specification to obtain a single set of estimated parameter means and variances. The single set of estimated means is simply the arithmetic average of the ten different estimation results. The single set of estimated variances is more complicated than a simple average be￾cause, as mentioned above, these variances account for both the ordinary within-sample variation and the between-sam￾ple variation due to missing data. See King et al. (2001) and Schafer (1997) for a complete description of these vari￾ances. Table 1 reports the summary statistics of our immigra￾tion-opinion measure and explanatory variables calculated by pooling together all ten of the imputed data sets for each year. The average value for Immigration Opinion was 3.60 in 1992, 3.98 in 1994, and 3.79 in 1996. The values reflect responses between "left the same as it is now" and "de￾creased a little." 13 TABLE 1 -SUMMARY STATISTICS Variable 1992 1994 1996 Immigration Opinion 3.595 3.982 3.785 (1.027) (1.064) (0.982) Occupation Wage 0.512 0.574 0.601 (0.187) (0.227) (0.225) Education Years 12.923 13.153 13.328 (2.815) (2.637) (2.660) Gender 0.534 0.534 0.552 (0.499) (0.499) (0.497) Age 45.755 46.264 47.544 (17.711) (17.646) (17.416) Black 0.129 0.115 0.122 (0.336) (0.319) (0.327) Hispanic 0.072 0.046 0.087 (0.259) (0.209) (0.282) Immigrant 0.181 0.166 0.147 (0.385) (0.371) (0.355) Party ID 3.701 3.916 3.673 (2.027) (2.102) (2.102) Ideology 4.237 4.446 4.275 (1.399) (1.348) (1.398) High Immigration MSA 0.235 0.227 0.215 (0.424) (0.419) (0.411) Number of observations 2485 1795 1714 These summary statistics are multiple-imputation estimates based on the ten imputed data sets for each year. Each cell reports the variable mean and (in parenthesis) its standard deviation. Occuipatiotn Wage reports the actual weekly wage divided by 1000. 10 For 1992, the variables included in the imputation model were Immigration Opinion, Occupation Wage, Education Years, Gender, Age, Black, Hispanic, Immigrant, Party ID, Ideology, High Immigration MSA, interactions of High Immigration MSA with skill measures, a continuous measure of percent immigrant in MSA/county of respondent, feeling thermometer scores for Hispanics and immigrants, family income, home ownership, union membership, retrospective evaluation of the national economy, retrospective evaluation of respondent's personal finances, three measures of respondent's tolerance, three responses to questions about the impact of Hispanic immigration on the United States, three responses to questions about the impact of Asian immigration on the United States, the respondent's view of welfare restrictions for immigrants, three measures of the skill composition of immigrants in the respondent's geographical location, and a sample weighting variable. For 1994 and 1996, these same variables, if available in the survey, were included. The variables for the imputation model were selected because they were included in the analysis models, were highly predictive of variables in the analysis model, or were highly predictive of the missingness in the data. 11 The imputation procedures were implemented using Amelia: A Pro￾gram for Missing Data (Honaker et al., 1999). 12 In this analysis, the imputation model was multivariate normal with a slight ridge prior. 13 For 1992, the exact breakdown of all responses to Immigration Opinion is as follows: 58 "increased a lot" (2.3% of the total sample, or 2,485); 116 "increased a little" (4.7%), 937 "left the same" (37.7%), 552 "decreased a little" (22.2%), and 505 "decreased a lot" (20.3%). In addition, we imputed responses for the 87 people (3.5%) who responded "don't know/no answer" and the 230 people (9.3%) who were not asked the question because of survey design. (All results reported in the paper are robust to excluding these 230 observations from the analysis.) We also note that the summary stati.stics in our data are similar to those obtained from the Current Population Survey (CPS). For example, in the 1992 CPS, This content downloaded from 202.120.14.193 on Mon, 15 Feb 2016 10:04:26 UTC All use subject to JSTOR Terms and Conditions