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1 ONLINE APPENDICES for How Well Do Automated Linking Methods Perform in Historical Samples? Evidence from New Ground Truth Martha Bailey, 1,2 Connor Cole, 1 Morgan Henderson, 1 Catherine Massey 1 1 University of Michigan 2 National Bureau of Economic Research February 24, 2018 [Click for Most Updated Paper] [Click for Most Updated Online Appendices] Online Appendix for How Well Do Automated Linking Methods Perform? 1

2 A. Details Regarding the Implementation of Algorithms and Effects of Race-Blocking 1. Implementation of s Method We generate links for the (2016) two ways. The Iowa coefficient results use the parameters that estimated with his training data that links the 1915 Iowa Census to the 1940 Census, which we directly apply to the relevant data ground truth sample. Because the performance of this algorithm hinges critically on the quality of the training data and its similarities with records we would like to link, we also examine performance based on coefficients that we estimate using a simple, random sample of the ground truth data used in this paper. For the Early Indicators data, we select a random sample of 500 observations. For all the other datasets, we select a random sample of 2,000 observations. (Our simulations show the size of the random sample has little effect on the outcomes above the sample size of 2,000). In each of these samples, we estimate a probit model on the training dataset using s covariates, with the outcome being the binary variable denoting a true match. Then, we apply the estimated parameters to the ground truth sample (less the training data) to classify links. Appendix Table A1 reports the estimation results using each ground truth sample. Column 1 presents the covariates reported by (2016) and the remaining columns present the coefficients for each ground truth sample. The parameter estimates vary somewhat, but the signs and magnitudes are similar across ground truth datasets. The missing variables in the probit reflect the fact that the relevant ground truth data either does not have variation in the variable or that the excluded variables perfectly predict matches or non-matches in the ground truth. Appendix Table 2 lists the other parameters that are relevant for s algorithm. Additionally, since the parameters estimated above are estimated with only a single random subset of the ground-truth, we report the average results from 200 repetitions of the algorithm. The b1 and b2 values are similar across datasets, with the exception of the IPUMS data. For IPUMS, the comparatively high value of b2 reflects the fact that IPUMS matches are likely more conservative. Across samples, the Type I and Type II error rates are similar across 200 repetitions in the ground truth. Online Appendix for How Well Do Automated Linking Methods Perform? 2

3 Appendix Table A1. Probit Coefficients Estimated Using Different Ground Truth Samples (1) (2) (3) (4) (5) Variables LIFE-M Simulated Early IPUMS-LRS (2016) Data Indicators First and Last Names Match 0.632*** 0.663*** * (0.086) (0.127) (0.0812) (0.172) (0.152) First Name Jaro-Winkler Score *** *** *** ** (0.525) (1.662) (1.058) (1.736) (2.059) Last Name Jaro-Winkler Score *** *** *** *** *** (0.487) (1.270) (0.826) (1.406) (1.735) Absolute Value of Difference in Year of Birth is *** *** *** *** (0.044) (0.0713) (0.0688) (0.114) (0.0970) Absolute Value of Difference in Year of Birth is *** *** *** *** *** (0.065) (0.113) (0.0700) (0.144) (0.526) Absolute Value of Difference in Year of Birth is *** *** *** - (0.102) (0.121) - (0.167) - First Name Soundex Match 0.153*** *** 0.715*** (0.054) (0.229) (0.137) (0.270) (0.273) Last Name Soundex Match 0.698*** 1.139*** 0.268*** 0.495*** 1.618*** (0.069) (0.145) (0.0938) (0.164) (0.370) Number of Potential Matches *** *** *** *** *** (0.002) ( ) ( ) ( ) ( ) Number of Potential Matches Squared **** 2.01e-05*** 5.34e-05*** 1.23e-05*** 7.51e-05*** ( ) (4.92e-06) (7.96e-06) (2.43e-05) (9.64e-06) More than One Exact Match on First and Last *** *** *** *** *** Name (0.093) (0.0754) (0.0576) (0.120) (0.153) First Letter of First Name Matches 0.871*** 1.004** 0.430*** (0.130) (0.434) (0.146) - (0.428) First Letter of Last Name Matches 0.886*** ** - (0.148) - (0.112) (0.273) - Last Letter of First Name Matches 0.147*** *** (0.053) (0.202) (0.140) (0.240) (0.234) Last Letter of Last Name Matches 0.649*** 0.382*** 0.942*** 0.542*** (0.070) (0.147) (0.118) (0.157) (0.205) Middle Initial Matches (0 if Middle Initial Does Not Exist or Does Not Match) 0.537*** 0.867*** 2.161*** 0.887*** 1.508*** (0.097) (0.0930) (0.0521) (0.154) (0.132) State is Ohio N/A 0.361*** 0.224*** N/A N/A (0.0656) (0.0505) Constant *** *** *** ** *** (0.225) (0.519) (0.289) (0.455) (0.669) Observations 38,091 42,973 50,255 6,582 43,960 Log-Likelihood Akaike Inf. Crit Notes: Column 2 drops the estimate for First Letter on Last Name, because LIFE-M blocked on this variable to create the list of potential links. Column 3 drops Absolute Value of Difference in Year of Birth is 3, because there is no variation in this. Column 5 drops Absolute Value of Difference in Year of Birth is 3 because IPUMS selected matches with 2 years gap or less; column 5 drops First letter on Last Name because there is no variation in this variable for IPUMS. Online Appendix for How Well Do Automated Linking Methods Perform? 3

4 Appendix Table A2. Features of the Classifier using the Estimated Coefficients (1) (2) (3) (4) (5) (2016) LIFE-M Simulated Data Early Indicators IPUMS- LRS B1 Value B2 Value Match Rate Type I Error Type II Error Average B1 Value Average B2 Value Average Match Rate Average Type I Error Average Type II Error Implementation of the Iterative Method The authors of the Iterative Method generously shared the most updated version of code used in et al. (2014), which was updated and posted here: We implement all algorithms using the code provided by the authors (labeled et al 2014 in Appendix Table A3). To implement et al. (2014), one must decide which dataset is the destfile and the sourcefile (the terms in Abramitsky et al. (2014) code shared with us are childfile and adultfile, respectively). The authors indicated in correspondence that the their 2014 paper uses the full Census data as the destfile and the sample file as the sourcefile, so we report these estimates using the same ordering in the main text of this paper. For the LIFE-M and synthetic data, the 1940 Census is the destfile and the birth certificate sample is the sourcefile. For the Early Indicators data, we make the UA Army Data the sourcefile and the 1900 Census data the destfile. For the IPUMS data, we make the non-1880 data the sourcefile and the 1880 full Census the destfile. This appendix presents two alternate specifications, including 1. et al. s (2014) robustness check that restricts both datasets to individuals with unique within a two-year age radius (-2, -1, 0, 1, 2; described as a five-year band in the paper). This check is a restriction that creates an un name-age sample, which is similar to the Ferrie (1996) Online Appendix for How Well Do Automated Linking Methods Perform? 4

5 method. 2. An alternative ordering that treats the Census file as the destfile and the non-census year as the sourcefile. This second specification is not published elsewhere, but the authors are aware of it. We present it to emphasize the importance of order for the Iterative Method with the existing publiclyavailable STATA code.since the code pre-emptively drops all duplicates name-age matches in the sourcefile, making a Census file the sourcefile may incorrectly link individuals from the destfile to the second-best link in the sourcefile. Consider the following example. Suppose that a smaller sample has been made the destfile and a Census the sourcefile, and there is one John Smith born in Ohio who would have been age 25 in the later year (the destfile ) but in the sourcefile there are three John Smiths born in Ohio age 25 (record 1-3 in the example below) and one John Smith born in Ohio age 27 (record 4) (and no other John Smith observations in the age range of 23-27). Since the Census is the sourcefile, the Iterative Method pre-emptively drops all John Smiths who are age 25 in the sourcefile and would link in error the sample John Smith age 25 to the Census John Smith age 27 (record 4), even though presumably better matches existed that were ruled out with the first step. On the other hand, if the Census is the destfile and the smaller sample the sourcefile, the code would not match the John Smith observation in the sourcefile to any of the observations in the Census since multiple potential exact links exist. Example Linking Problem where Order Matters destfile sourcefile destfile Birthplace Age Record sourcefile Birthplace Name number Name Age 1 John Smith OH 25 John Smith OH 25 2 John Smith OH 25 3 John Smith OH 25 4 John Smith 27 Choices about which file is the sourcefile and destfile are, therefore, consequential for error rates and may be more consequential in settings where the sample files are generally much smaller than a population Online Appendix for How Well Do Automated Linking Methods Perform? 5

6 enumeration. It would be less consequential in settings where researchers are linking full populations to one another, because multiple John Smiths would likely appear in both files and, therefore, be eliminated as matches. Note that the robustness check with the two-year radius eliminates this problem: in our example, it would drop all of the John Smith observations in the sourcefile. The table A3.A and A3.B demonstrate how match and error rates change as with the choice of which file is the sourcefile. Online Appendix for How Well Do Automated Linking Methods Perform? 6

7 Appendix Table A3.A. Summary of Match and Error Rates for Linking with Census as destfile, by Ground Truth et al Baseline A. Match Rates B. Type I Error Rate (False Links) C. Type II Error Rate (Missed links) LIFE-M Synthetic EI IPUMS- LRS LIFE-M Synthetic EI IPUMS- LRS LIFE-M Synthetic EI Name NYSIIS SDX et al 2014 Robustness Check Name NYSIIS SDX IPUMS- LRS Appendix Table A3.B. Summary of Match and Error Rates for Linking with Census as sourcefile, by Ground Truth et al Baseline A. Match Rates B. Type I Error Rate (False Links) C. Type II Error Rate (Missed links) LIFE-M Synthetic EI IPUMS- LRS LIFE-M Synthetic EI IPUMS- LRS LIFE-M Synthetic EI Name NYSIIS SDX et al 2014 Robustness Check Name NYSIIS SDX IPUMS- LRS Notes: In Table A3.A, we treat the Census file as the childfile (or destfile ) in the code. In Table A3.B, we treat the Census file as the adultfile (or sourcefile ). EI stands for the Early Indicators data. Baseline refers to the primary matching algorithm used in. Robustness refers to specifications where both the original dataset and the data being linked to are limited to unique name combinations within a five-year age band prior to linkage. Online Appendix for How Well Do Automated Linking Methods Perform? 7

8 B. Description of LIFE-M Data The LIFE-M samples used in this paper are based on the first two years of hand-linking in this project. This section supplements the description in the paper. 1. Determining Sex Because it was the norm for girls to change their name at marriage and around 90 percent of surviving girls married in the middle of the 20 th century, we only attempt to link male infants to their records in the 1940 Census. In some cases, sex is missing or apparently incorrect. To determine which of these records were very likely to be boys, we generated an empirical distribution of sex and first using all vital records in the LIFE-M collection. We use this distribution to classify as male if there were at least 50 records with the name and at least 99 percent of the records with that name were female. If there was ambiguity about whether the infant was a boy, we did not attempt to link the record. This is why fewer than 50 percent of the records in Ohio (and especially North Carolina) were male. 2. Constructing Samples of Male Birth Certificates To construct this data for Ohio, we drew a random sample of 13,270 birth certificates for individuals born in Ohio from 1909 to 1920: a 2 percent sample of 1909 and a 1-percent sample each year between 1910 and Next, sets of parents for these infants were linked to parents of other infants using the first and birth name of both fathers and mothers (four distinct fields), thus recovering siblings for each sampled birth certificate. The final sample of reconstructed families consists of 53,721 children, 19,090 of which were determined to be boys (see discussion above). Appendix Figure C1 plots the distribution of age in 1940 for the 19,090 Ohio boys. To construct the North Carolina data, we drew a random sample of 23,073 birth certificates for individuals born in North Carolina from 1915 to (These sampling years differ from Ohio due to the incompleteness of the North Carolina birth data before 1915). We used the same process as in Ohio to link parents to identify siblings. This resulted in a total sample of 86,209 infants, 26,352 of whom we determined to be boys (see discussion above). Appendix Figure C1 shows the distribution of age in 1940 Online Appendix for How Well Do Automated Linking Methods Perform? 8

9 for these 26,352 boys. 3. Linking Birth Certificate Samples to the 1940 Census A final step linked the Ohio and North Carolina samples to the 1940 Census using the process described in the paper. During the hand-linkage process, each potential link was initially reviewed by two trainers in a double-blind review process. If these trainers agreed on whether to link or not to link a case, we take their decision as the truth. If they disagreed, an additional three additional trainers reviewed the record. We take records for which 4/5 of the trainers agreed as a match, the presumption being that one of the original trainers made an error. The first two data trainers disagreed 10 percent of the time for male infants in Ohio and 8.3 percent of the time for male infants in North Carolina. Ohio Births Appendix Figure B1. Distribution of Boys Age in 1940 North Carolina Births Age Age Online Appendix for How Well Do Automated Linking Methods Perform? 9

10 C. Representativeness Regression Results Appendix Table C1. Representativeness Results for LIFE-M LIFE-M Feigenbau m 2016 (Iowa Feigenbau m 2016 (estimated Day of Birth *** *** *** *** *** *** *** *** *** *** *** * *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Number of Siblings *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Length of Child's Name *** *** *** *** *** *** *** *** ** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Length of Father's Name *** *** *** *** ** *** *** ** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Length of Mother's Name *** *** *** *** ** *** *** ** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Share of Observations with * ** * *** * ** Misspelled Mother's Name ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Share of Observations with *** ** *** *** ** *** *** ** *** *** * *** * *** ** Misspelled Father's Name ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Link in North Carolina *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Constant *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Observations 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 43,417 R-squared Wald Statistic Prob > W Note: Robust standard errors are in parentheses. Regressions are a test of representativeness in the LIFE-M data by regressing for all observations in the master data a dummy variable indicating whether or not an observation was matched on the variables included in this table. The Wald statistic at the end offers a test of whether or not matched status systematically relates to covariates. Online Appendix for How Well Do Automated Linking Methods Perform? 10

11 Appendix Table C2. Representativeness Results for Synthetic Data LIFE-M Feigenbau m 2016 (Iowa Feigenbau m 2016 (estimated Day of Birth ** * *** *** * *** *** ** ** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Number of Siblings *** *** *** *** *** *** *** *** *** ** * *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Length of Child's Name ** *** ** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Length of Father's Name *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Length of Mother's Name *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Share of Observations with ** ** ** Misspelled Mother's Name ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Share of Observations with *** *** *** ** *** *** ** *** *** *** *** *** *** Misspelled Father's Name ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Link is in North Carolina *** *** * *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Constant *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Observations 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 45,417 43,417 R-squared Wald Statistic Prob > W Note: Robust standard errors in parentheses. Regressions are a test of representativeness in the synthetic data by regressing for all observations in the master data a dummy variable indicating whether or not an observation was matched on the variables included in this table. The Wald statistic at the end offers a test of whether or not matched status systematically relates to covariates. Online Appendix for How Well Do Automated Linking Methods Perform? 11

12 Appendix Table C3. Representativeness Results for Early Indicators Ferrie 1996 Ferrie Qian 2015 Qian (Iowa 2016 (estimated Age 0.01* * *** 0.020*** 0.019*** 0.013** 0.011* (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) (0.006) (0.006) (0.005) (0.007) (0.006) (0.006) (0.007) Is Currently Married 0.08** * (0.037) (0.037) (0.037) (0.038) (0.038) (0.038) (0.037) (0.038) (0.038) (0.038) (0.037) (0.036) (0.037) (0.043) Foreign Born ** *** ** (0.053) (0.052) (0.048) (0.053) (0.054) (0.054) (0.052) (0.053) (0.054) (0.053) (0.052) (0.051) (0.053) (0.060) Day of Birth * (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Literate 0.15** 0.129** 0.100* *** 0.241*** 0.249*** Length of First Name Length of Second Name (0.062) (0.062) (0.060) (0.067) (0.067) (0.067) (0.065) (0.067) (0.067) (0.066) (0.067) (0.069) (0.064) (0.076) 0.02* 0.023*** 0.032*** * 0.023*** *** (0.008) (0.008) (0.008) (0.009) (0.009) (0.009) (0.008) (0.009) (0.009) (0.009) (0.009) (0.008) (0.008) (0.010) -0.03*** 0.020*** 0.023*** *** *** *** *** *** (0.007) (0.007) (0.007) (0.007) (0.007) (0.007) (0.007) (0.007) (0.007) (0.007) (0.007) (0.007) (0.007) (0.008) Mother is Foreign Born -0.12** ** ** *** *** (0.053) (0.053) (0.052) (0.053) (0.053) (0.055) (0.054) (0.053) (0.055) (0.052) (0.049) (0.050) (0.051) (0.059) Father is Foreign Born ** (0.051) (0.050) (0.050) (0.051) (0.050) (0.052) (0.052) (0.051) (0.052) (0.050) (0.047) (0.047) (0.048) (0.055) Year of Birth *** 0.019*** 0.018*** (0.005) (0.005) (0.005) (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) (0.005) (0.007) (0.006) (0.007) (0.007) Constant ** *** *** (9.951) (10.399) (10.107) (10.558) (10.839) (10.935) (10.872) (11.465) (11.410) (10.400) (13.631) (12.049) (12.459) (13.009) Observations 1,774 1,774 1,774 1,774 1,774 1,774 1,774 1,774 1,774 1,774 1,774 1,774 1,774 1,343 R-squared Wald Statistic Prob > W Note: Robust standard errors in parentheses. Regressions are a test of representativeness in the Early Indicators data by regressing for all observations in the master data a dummy variable indicating whether or not an observation was matched on the variables included in this table. The Wald statistic at the end offers a test of whether or not matched status systematically relates to covariates. Note that the representativeness of the data are measured against the universe of high quality links stated by the Early Indicators project for the Oldest Old sample. Online Appendix for How Well Do Automated Linking Methods Perform? 12

13 Appendix Table C4. Representativeness Results for IPUMS-LRS IPUMS (Iowa 2016 (estimated Number of *** *** *** *** *** ** *** ** *** *** *** *** *** ** Siblings ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Age *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Lives with *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** Mother ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Lives with *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** Father ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Lives with *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** Both Parents ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Father: Born ** *** *** *** *** *** *** *** *** *** *** *** Abroad ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Mother: Born *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** Abroad ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Lives in *** *** *** *** *** *** *** *** *** ** *** *** Northeast ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Lives in *** *** *** *** *** *** *** *** *** *** *** *** *** *** Midwest ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Lives in West *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Farm Status *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Married *** *** *** *** *** *** ** *** *** *** ** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) White Collar *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** Occupation ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Farming *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** Occupation ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Semi-Skilled *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** Occupation ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Online Appendix for How Well Do Automated Linking Methods Perform? 13

14 Appendix Table C4. Representativeness Results for IPUMS-LRS - Continued IPUMS (Iowa 2016 (estimated Unskilled *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** Occupation ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) White *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Urban Status *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Born Abroad *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Constant *** *** *** ** *** ** ** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Observations 32,959,605 32,959,605 32,959,605 32,959,605 32,959,605 32,959,605 32,959,605 32,959,605 32,959,605 32,959,605 32,959,605 32,959,605 32,959,605 32,959,605 32,959,605 R-squared Wald Statistic Prob > W Note: Robust standard errors in parentheses. Regressions are a test of representativeness in the IPUMS data by regressing for all observations in the final year data (e.g for matches from 1880 to 1900) a dummy variable indicating whether or not an observation was matched on the variables included in this table from that final year. The Wald statistic at the end offers a test of whether or not matched status systematically relates to covariates. The IPUMS sample sizes are different than other regressions because, in order to use the weights provided by IPUMS, we use the one percent sample for all matches involving 1880 as this sample was what was used to initially construct weights. Other than the 'IPUMS - Weighted' results, all other tests are unweighted and use the complete 1880 Census for matches from earlier years to the 1880 Census. Since we only match individuals who were plausibly 0-15 in the base year, we restrict attention here to men who would plausibly be that age in the final year (e.g. in matching from 1850 to 1880, we restrict attention to men aged in 1880). For concision, we stack all years for a single test. Additional results that break down test results by year are available by request. Online Appendix for How Well Do Automated Linking Methods Perform? 14

15 D. Correlation of Incorrect Links with Baseline Sample Characteristics Appendix Table D1. Correlation of Incorrect Links with Baseline Sample Characteristics in LIFE-M Data LIFE-M (Iowa 2016 (estimated Day of Birth *** *** * *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Number of Siblings * *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Length of Child's Name ** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Length of Father's Name *** *** *** *** * *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Length of Mother's Name *** *** *** *** *** *** ** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Share of Observations with ** Misspelled Mother's Name ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Share of Observations with *** *** *** *** *** ** Misspelled Father's Name ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Link in North Carolina *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Constant *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Observations 19,391 13,865 11,762 8,494 19,703 19,572 17,656 17,646 17,894 16,722 30,520 34,553 37,145 21,310 19,323 R-squared Wald Statistic Prob > W Note: Robust standard errors in parentheses. Regressions are a test of correct matches in the LIFE-M data by regressing for matches by each matching strategy a dummy variable indicating whether or not an observation was correctly matched (as determined by the LIFE-M 'police line-up' review process described in the paper) on the variables included in this table. The Wald statistic at the end offers a test of whether or not correct matches compared to incorrect matches systematically relate to covariates. Online Appendix for How Well Do Automated Linking Methods Perform? 15

16 Appendix Table D2. Correlation of Incorrect Links with Baseline Sample Characteristics in Simulated Data (Iowa 2016 (estimated Day of Birth ** ** ** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Number of Siblings * *** ** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Length of Child's Name * * ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Length of Father's Name ** ** * ** *** * ** *** *** *** *** *** ** ** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Length of Mother's Name ** *** *** *** ** *** *** *** *** ** *** Share of Observations with Misspelled Mother's Name Share of Observations with Misspelled Father's Name Link is in North Carolina Constant ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) * ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) * ** *** *** * *** *** * *** *** *** ** ** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) *** ** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Observations 14,107 12,254 9,287 19,383 19,818 18,722 17,316 18,196 17,849 30,852 35,720 39,368 25,020 26,146 R-squared Wald Statistic Prob > W Note: Robust standard errors in parentheses. Regressions are a test of correct matches in the synthetic data by regressing for matches by matching strategy a dummy variable indicating whether or not an observation was correctly matched (as determined by the process used to create the synthetic data initially) on the variables included in this table. The Wald statistic at the end offers a test of whether or not correct matches compared to incorrect matches systematically relate to covariates. Online Appendix for How Well Do Automated Linking Methods Perform? 16

17 Appendix Table D3. Correlation of Incorrect Links with Baseline Sample Characteristics in Early Indicators Ferrie 1996 Ferrie 1996 Ferrie Qian 2015 Qian (Iowa 2016 (estimated Age -0.02** ** *** *** *** *** *** *** ** * * *** ** (0.010) (0.010) (0.010) (0.008) (0.008) (0.008) (0.009) (0.009) (0.010) (0.010) (0.007) (0.009) (0.008) (0.008) Is Currently Married (0.044) (0.045) (0.051) (0.046) (0.045) (0.049) (0.046) (0.046) (0.049) (0.045) (0.044) (0.046) (0.037) (0.045) Foreign Born (0.078) (0.078) (0.091) (0.075) (0.074) (0.078) (0.077) (0.075) (0.078) (0.073) (0.068) (0.065) (0.059) (0.071) Day of Birth ** * ** ** * ** ** ** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Literate ** *** * *** ** * (0.106) (0.105) (0.115) (0.095) (0.088) (0.091) (0.101) (0.097) (0.096) (0.105) (0.101) (0.092) (0.076) (0.091) Length of First Name -0.02* * ** ** *** (0.012) (0.012) (0.013) (0.012) (0.012) (0.012) (0.012) (0.012) (0.011) (0.011) (0.011) (0.011) (0.010) (0.012) Length of Second Name ** ** *** ** (0.009) (0.010) (0.010) (0.009) (0.009) (0.009) (0.009) (0.009) (0.010) (0.009) (0.009) (0.009) (0.007) (0.008) Mother is Foreign Born * * (0.070) (0.073) (0.086) (0.068) (0.072) (0.073) (0.068) (0.075) (0.076) (0.064) (0.064) (0.065) (0.055) (0.066) Father is Foreign Born (0.055) (0.059) (0.072) (0.056) (0.060) (0.065) (0.055) (0.063) (0.068) (0.059) (0.059) (0.060) (0.048) (0.060) Year of Birth *** ** ** *** *** ** ** (0.010) (0.010) (0.010) (0.008) (0.008) (0.009) (0.009) (0.009) (0.010) (0.010) (0.007) (0.009) (0.008) (0.008) Constant *** ** ** *** *** ** ** * (19.173) (18.999) (19.516) (14.834) (15.231) (16.257) (17.144) (17.324) (19.130) (18.618) (14.057) (17.912) (15.552) (15.846) Observations ,124 1,198 1, R-squared Wald Statistic Prob > W Note: Robust standard errors in parentheses. Regressions are a test of correct matches in the Early Indicators data by regressing for matches a dummy variable indicating whether or not an observation was correctly matched (as determined by the matches from the Early Indicators data) on the variables included in this table. The Wald statistic at the end offers a test of whether or not correct matches compared to incorrect matches systematically relate to covariates. Online Appendix for How Well Do Automated Linking Methods Perform? 17

18 Appendix Table D4. Correlation of Incorrect Links with Baseline Sample Characteristics in IPUMS-LRS IP UMS (Iowa 2016 (estimated Number of *** *** *** *** *** *** *** *** *** *** *** *** *** *** Siblings (0.0007) (0.0010) (0.0010) (0.0011) (0.0009) (0.0008) (0.0009) (0.0009) (0.0009) (0.0009) (0.0008) (0.0007) (0.0007) (0.0010) (0.0013) Age * *** *** *** *** *** *** *** *** *** Lives with Mother Lives with Father Lives with Both Parents Father: Born Abroad Mother: Born Abroad Lives in Northeast Lives in Midwest Lives in West (0.0002) (0.0003) (0.0003) (0.0003) (0.0002) (0.0002) (0.0002) (0.0002) (0.0002) (0.0002) (0.0002) (0.0002) (0.0002) (0.0003) (0.0004) *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** (0.0047) (0.0062) (0.0062) (0.0068) (0.0053) (0.0050) (0.0052) (0.0058) (0.0054) (0.0054) (0.0048) (0.0043) (0.0041) (0.0067) (0.0096) *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** (0.0068) (0.0097) (0.0094) (0.0106) (0.0083) (0.0078) (0.0081) (0.0090) (0.0082) (0.0085) (0.0077) (0.0068) (0.0066) (0.0098) (0.0134) ** * *** *** * *** ** ** *** (0.0077) (0.0110) (0.0107) (0.0120) (0.0095) (0.0089) (0.0093) (0.0103) (0.0094) (0.0097) (0.0088) (0.0077) (0.0075) (0.0111) (0.0152) *** *** *** * *** *** *** *** (0.0041) (0.0064) (0.0064) (0.0074) (0.0059) (0.0056) (0.0059) (0.0063) (0.0059) (0.0062) (0.0054) (0.0048) (0.0046) (0.0081) (0.0115) *** *** *** *** *** *** *** *** *** *** *** *** *** *** (0.0045) (0.0067) (0.0067) (0.0078) (0.0062) (0.0058) (0.0062) (0.0066) (0.0061) (0.0065) (0.0057) (0.0050) (0.0047) (0.0084) (0.0119) *** *** *** *** *** *** *** *** *** *** *** *** *** *** (0.0032) (0.0041) (0.0041) (0.0045) (0.0035) (0.0034) (0.0035) (0.0039) (0.0036) (0.0036) (0.0033) (0.0030) (0.0029) (0.0048) (0.0065) *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** (0.0033) (0.0041) (0.0041) (0.0045) (0.0036) (0.0034) (0.0035) (0.0040) (0.0036) (0.0036) (0.0033) (0.0029) (0.0028) (0.0046) (0.0063) ** *** *** *** *** *** *** *** *** *** *** *** *** *** *** (0.0064) (0.0079) (0.0077) (0.0080) (0.0069) (0.0064) (0.0063) (0.0077) (0.0068) (0.0066) (0.0064) (0.0056) (0.0052) (0.0099) (0.0132) Farm Status ** * ** ** ** *** * *** ** (0.0036) (0.0045) (0.0045) (0.0050) (0.0039) (0.0037) (0.0038) (0.0043) (0.0039) (0.0040) (0.0036) (0.0032) (0.0031) (0.0049) (0.0068) Married *** *** *** *** *** *** *** *** *** *** *** *** *** *** White Collar Occupation Farming Occupation Semi-Skilled Occupation (0.0040) (0.0046) (0.0046) (0.0049) (0.0039) (0.0036) (0.0036) (0.0043) (0.0039) (0.0038) (0.0034) (0.0030) (0.0028) (0.0058) (0.0084) *** *** *** *** *** *** *** *** *** *** *** *** *** * (0.0047) (0.0063) (0.0063) (0.0070) (0.0055) (0.0052) (0.0054) (0.0059) (0.0055) (0.0056) (0.0051) (0.0046) (0.0044) (0.0071) (0.0097) *** *** *** ** ** (0.0052) (0.0067) (0.0065) (0.0073) (0.0058) (0.0055) (0.0057) (0.0063) (0.0058) (0.0059) (0.0054) (0.0048) (0.0046) (0.0071) (0.0097) *** *** ** *** ** * *** ** ** ** ** (0.0046) (0.0058) (0.0058) (0.0064) (0.0050) (0.0047) (0.0049) (0.0054) (0.0050) (0.0051) (0.0046) (0.0041) (0.0039) (0.0064) (0.0089) Online Appendix for How Well Do Automated Linking Methods Perform? 18