Record Linkage For Character-Based Surnames: Evidence from Chinese Exclusion

Abstract

This paper proposes a novel pre-processing technique to improve record linkage for historical Chinese populations. Current matching approaches are relatively ineffective due to Chinese-specific naming conventions and enumeration errors. This paper develops a three-step process that both triples the match rate over baseline and improves match accuracy. The procedures developed in this paper can be applied in part or in full to other sources of historical data, and/or modified for use with other character-based languages such as Japanese. More broadly, this approach suggests the promise of language-specific linkage procedures to boost match rates for ethnic minority groups.

1. Introduction

Historical record linkage entails finding the same individual in two or more datasets (typically censuses) using characteristics such as names, birthplaces, and ages. Multiple automated algorithms have been developed to maximize the accuracy and efficiency of such efforts. These methods generally link between 25% and 50% of the overall population but are not equipped to handle the especially poor and uneven name transcription present for foreign-born individuals from non-English speaking countries (Abramitzky et al. 2021; Helgertz et al. 2022). These issues are particularly grave for non-Romanized names.

This project addresses the challenge of low match rates for Chinese immigrants in historical census data. A standard matching approach finds only 3.6% of Chinese men living in the United States in 1880 again in 1900, compared to 10.3% of Germans, 11.2% of Irish, and 16.3% of English.¹ These low match rates both bias overall linked samples and preclude learning about uniquely Chinese experiences in economic history. For example, Chinese immigrants in the United States were particularly central to debates around federal immigration control in the late 19^th and early 20^th centuries. The ability to link this group over time would both illuminate how immigration restrictions impacted Chinese communities specifically and contribute to a broader understanding of immigration policy effects.

I develop a three-step pre-processing approach to increase successful record linkage for immigrant communities with character-based names in the context of late 19^th-century Chinese Exclusion laws. My procedure triples the match rate over a standard approach, bringing the share of linked Chinese level with that for European immigrant groups. This project focuses on linking Chinese-born individuals between the 1880 and 1900 censuses but can also be applied to other historical data sources.

The matching approach outlined in this paper is highly adaptable. It can be used in tandem with any matching algorithm, implemented in full or in part, and customized for use depending on the available data. It can also be modified for use with other character-based languages (e.g. Japanese) to enable quantitative analysis of other historically understudied communities. Most foundationally, it highlights both the necessity and the promise of linguistically tailored matching approaches for immigrant groups. Both the code and the dictionary crosswalk are publicly available on Dataverse (Postel 2022).

The paper proceeds as follows. Section 2 outlines three major factors influencing low match rates for Chinese immigrants. Section 3 details the steps taken to address these challenges and presents the resulting linked data. Section 4 assesses the robustness and accuracy of the proposed approach (“Postel method”) in another year pair and by comparison to standard matching algorithms. Section 5 concludes.

2. Three Factors Contributing to Low Match Rates

Chinese is a logographic language comprised of non-phonetic symbols (“characters”). Words (including names) can be composed of multiple characters. Contrary to many Western naming conventions, in Chinese the surname traditionally precedes the given name.² Though the Beijing dialect (Mandarin) is now accepted as the modern Chinese language standard, until the 1920s a large number of mutually unintelligible dialects were spoken across the country. And not until 1958 did the Chinese government institute a systematic method for transliterating characters into the Roman alphabet (hànyŭ pīnyīn, “spelled sounds of the spoken language of the Han people”) (Chen 1999).

U.S. census enumerators were generally unaware of these linguistic specificities. Though relatively few details on historical enumeration procedures exist, as of 1950 enumerators were instructed to “enter first the surname, then the given name in full, and the initial of the middle name, if any” (Census 1950). It is likely that enumerators recorded names either exactly as they heard them or with oral spelling assistance from the respondent.³

The combination of these factors produced widespread errors in three realms of Chinese name enumeration: segmentation, name order, and standardization. Many of these enumeration issues were compounded when census pages were indexed (digitized for entry into database format). The following sections explore each challenge in turn.

2.1. Segmentation

The fact that Chinese words can – but do not always – consist of multiple individual characters poses a challenge when “translating” between Chinese characters and Romanized spellings. Word segmentation is therefore often the first step in Chinese natural language processing tasks (Chang et al. 2008). This issue is particularly evident when looking at how Chinese names were indexed in full-count census databases. For example, in one Utah county, two individuals were enumerated and indexed as follows.

Comparing Figure 1 to Table 1 shows that these names were erroneously indexed. Name fragments were all kept together in a single column rather than being allocated across “first” and “last” name columns. Though this issue is relatively unique to individuals with Chinese and other character-based names (as allocating e.g. “John” and “Smith” to the correct name columns was likely straightforward), for these populations such errors were widespread. Fully 79% of Chinese individuals in the 1880 census data are missing either a first or last name as indexed.

Figure 1:

Chinese names as enumerated in the 1880 census

Table 1:

Chinese names as indexed

First Name	Last Name
—	Fong Lu Cong
Hang Lee	—

These segmentation errors pose massive challenges to record linkage, as matching algorithms compare potential matches’ first names to first names and last names to last names. It is therefore extremely difficult to match individuals who are missing data in either column. This challenge is compounded by the fact that which name column is missing data was inconsistent even within small geographic designations. And the likelihood of consistent mis-segmentation across time is low, given that segmentation issues are less common in later census years.

2.2. Name order

Historical census enumerators were unsure about the order in which to record Chinese names; in fact, “it is only when Chinese characters are available that you can be sure of the position of the surname in a Chinese personal name” (Louie 2008, 86). This led to enumerators “accustomed to European names” recording Chinese names in many “odd ways” (Jones 1997, 31). It is therefore unclear in which order Chinese names were enumerated (i.e. according to Chinese or Anglo conventions), and unlikely name ordering practices were consistent across time or space.

2.3. Standardization

Incorrect name transcriptions occur throughout the census, particularly for recent immigrants whose names “were sometimes garbled by enumerators who had difficulty understanding foreign accents” (United States National Archives 2021). For Chinese immigrants, these difficulties were compounded by a lack of standardized procedure for either pronouncing Chinese characters or transliterating them to the Roman alphabet.

As mentioned above, prior to 1932 there was no standardized form of spoken Chinese. This linguistic diversity was particularly prevalent among Chinese immigrants to the United States, most of who came from southeastern Chinese provinces where multiple dialects were spoken including Cantonese (Yue), Hakka, and Min (Lai 1991). How names were recorded by census enumerators therefore likely reflected different pronunciations across dialects.

The lack of a unified method to transliterate Chinese characters into the Roman alphabet also meant that a single character could be transliterated in many different ways. For example, the surname 杨 (yáng in pinyin) was variously recorded as Young, Yeo, Yong, Yeung, Yeang, and Yung (Louie 2008, 190).

A 1991 report for National Archives researchers provides census-specific validation of the above challenges (emphasis added):

“There were also unintentional cultural barriers that stood between Chinese and the census process. For example, immigration documents bearing Chinese characters have revealed instances of the same Chinese surname transliterated as Jung, Chung and Chong, depending on the pronunciation of the Chinese and the whim of whoever was recording it. Moreover, another surname which was unrelated to the first was also found to be spelled Jung.

This is only one example of many potential obfuscations. There was no standard method to transliterate Chinese, and census takers often wrote what they believed they heard, particularly if the Chinese could not write English well. The result is that members of the same family or even the same individual at different times could be recorded with different transliterations of their surnames, while members of different families could be recorded with the same transliterations” (McGlinn 1991, 119).

This description reaffirms that the lack of a systematic Chinese transliteration scheme in combination with enumerator- and respondent-side issues yielded artificially inflated variation in census transcriptions of Chinese names.

2.4. Comparison with existing name-cleaning approaches

Low match rates are perhaps not surprising in view of these many challenges: the underlying data quality for historical Chinese immigrants in the U.S. Census is much lower than for other groups. But modern research approaches (in the form of record linkage algorithms) also contribute to low linkage rates by mishandling Chinese names.

Most fundamentally, by relying on linking first names to first names and last names to last names as indexed, these approaches are highly vulnerable to errors in segmentation and name ordering. A drastic example occurs in how the Abramitzky, Boustan, and Eriksson (ABE) algorithm’s built-in name cleaning procedure handles multi-part names. In most cases, names with more than one fragment are cleaned to drop all but first fragment. This means that the 1,625 multi-part raw names including “Chin” (e.g. “Chin Fung”, “Chin Hing”, “Chin Lung”) are all condensed to simply “Chin” after cleaning. This not only overcondenses multiple-part names, but also makes them equivalent to the 417 individuals listed with only “Chin” as a first name. This issue is particularly dire given the widespread name segmentation issues in the 1880 census.

Existing record linkage algorithms also all involve some form of name standardization, employed to harmonize multiple variations of the same person’s name (through e.g. remedying inconsistent spellings, standardizing abbreviations, and applying nickname equivalents). Unfortunately, these procedures – both phonetic and string-based – do not work well in Chinese. ABE employs a phonetic similarity algorithm (NYSIIS) that tends to over-condense Chinese surnames (Li et al. 2018). For example, the distinct surnames “Yang”, “Ying”, and “Young” are all standardized as “yang”. Two other approaches (the Multigenerational Longitudinal Panel (MLP) and BYU Census Tree) employ string distance measures, which often designate two Chinese names as different when they in fact share the same underlying character (Peng et al. 2015).

The procedure outlined below addresses each of the above issues to boost both match rate and match accuracy for historical Chinese populations. It links 7,345 individuals between the 1880 and 1900 censuses (9.6% of the 1900 population), performing similarly well in a different year pair (see Section 4). This represents a three-fold increase over a standard baseline match. All data and code are available online (Postel 2022).

3. Matching Approach and Results

This paper develops a three-step pre-processing approach for character-based names to be iteratively applied with the researcher’s choice of record linkage algorithm. For the sake of clarity, this paper uses only the fully automated ABE standard matching approach but can be used – in part or in full – with any other algorithm.

I use the 1880 and 1900 full-count census data provided by IPUMS and accessed via the National Bureau of Economic Research.⁴ My data consist of men born in China and designated to be of Chinese race living in the continental United States: 97,970 in 1880 and 76,484 in 1900.⁵ The significant population decrease can be attributed to the restrictive and increasingly stringent Chinese Exclusion laws implemented during this period (see e.g. Salyer 1995).

I conduct a baseline match following basic name cleaning procedures including replacing special characters, trimming spaces, and standardizing common name spellings.⁶ 2,418 individuals are linked at baseline for a match rate of 3.2%.⁷

3.1. Segmentation

The first step of this paper’s proposed approach addresses segmentation errors by consistently delimiting name fragments within their indexed first- and last-name columns. I ensure each name fragment (here conceptualized as single Chinese character) is separated by a space within the indexed column, next segmenting each fragment into its own column (shown in Table 2 below).⁸ In the example of “Fong Lu Cong” from Utah above, “Fong”, “Lu”, and “Cong” are each individual fragments.

Table 2:

Segmenting multi-part names into individual fragments

As transcribed			After name splitting
First name	Last name		Name1	Name2	Name3	Name4
—	Fong Lu Cong		Fong	Lu	Cong	.
Hang Lee	—		Hang	Lee	.	.

A standard ABE match conducted following this segmentation step compares each name fragment among potential matches (e.g. “Name 1” with “Name 1”, “Name 2” with “Name 2”, etc). This step links 2,225 additional individuals – a 92% increase over baseline – for a total of 4,643 linked pairs.

3.2. Name order

Step 2 attempts to remedy inconsistent name order enumeration. I do so by changing the order of the name fragments created in the previous step for one year’s data only. Specifically, this step matches the original 1880 name fragments to a 1900 dataset with name fragments listed in a different order.

I conduct this approach separately for two- and three-fragment names.⁹ In the simple case of a two-fragment name, “Hang Lee” would be left identical to the previous step in 1880 and reversed to “Lee Hang” in 1900. I change the order for three-fragment names in two ways reflecting the fact that most Chinese surnames consist of only one character.¹⁰ Suppose an individual in 1900 was enumerated as Ping Deng Xiao. The accurate surname is likely listed as either fragment one (“Peng”) or fragment three (“Xiao”), since a single-character family name would be enumerated either first or last. I therefore try matching after converting this individual’s name first to Xiao Ping Deng and next to Deng Xiao Ping (which we know to be the correct order in the case of a former Chinese leader).

The step links an additional 2,193 individuals for a running total of 6,836 matched pairs.

3.3. Standardization

Finally, I conduct name standardization customized for Chinese names. The goal of this step is to minimize artificially inflated variation in indexed names by mapping Romanized spellings to their equivalent Chinese character. This is essentially a form of dimension reduction based on the linguistic traits described in Section 2.3 above.

I draw on a historical database of Chinese immigration files to compile a standardization crosswalk consisting of equivalencies between Romanizations and characters. This step focuses on surnames, as the number of potential character mappings is at least an order of magnitude smaller.¹¹

3.3.1. Creating a crosswalk

My historical data source is a digitized index of Chinese Exclusion case files covering the New York region. Chinese immigrants to the United States had to complete and sign many application forms upon entry and exit; these signatures were often recorded in both Romanized and Chinese character formats, as shown in Figure 2 below.

Figure 2:

Ho Young Exclusion file

This index – accessed at the U.S. National Archives’ New York City branch – consists of 18,533 individuals. 60% are listed with surnames in both Romanized and character forms. Following a validation process described in Appendix A.2, I merge the Exclusion File index with the Unihan database, which “contains mapping data to allow conversion to and from other coded character sets” based on Chinese ideographic script.¹²

The final product is a crosswalk of character mappings for each Romanized name. I calculate the total number of each Romanized surname in the New York database and the frequency of each identified character mapping. Table 3 below gives two examples.

Table 3:

Excerpt from character-equivalent crosswalk

Name1	N1_freq	C1_utf	C1-py	C1_freq	C1_prop	C2_utf	C2_py	C2_freq	C2_prop
Ho	49	U+4F55	hé	49	1.00	.	.	.	.
Fong	137	U+65B9	fāng	67	.489	U+913A	zhào	31	.229

Notes. The column N1_freq lists the total number of times a specific Romanization appeared in the New York Exclusion File index; C*_freq the number of times a character was mapped to said Romanization. C*_prop calculates the frequency with which a character maps to a Romanization; C*_utf and C*_py list the character in its UTF-8 and pinyin forms, respectively.

The surname “Ho” appears 49 times in the index and each time is identified as corresponding to the character 何 (hé in pinyin). By contrast, “Fong” appears 137 times and is mapped to multiple characters (three in total, with the two most frequent mappings displayed in the table).

3.3.2. Applying crosswalk to census data

The next step is to apply the name crosswalk to the census data. In some cases this is straightforward, such as for surname “Ho”. For cases such as “Fong”, however, there is no dispositive character equivalent as even the most common character mapping occurs for less than half of cases.

I propose using the listed frequencies to inform a decision rule on when to apply a character equivalent to a Romanized name. Given that some Romanizations match to more than one character, the mapping frequencies can serve as a threshold over which the user “trusts” the character mappings of choice. This analysis specifies a cutoff of 0.7 but alternative thresholds could be employed.¹³ After applying the crosswalk to each census year and replacing relevant names with their character equivalent (in UTF-8 format), an additional matching attempt is made. This step identifies an additional 509 matched pairs.¹⁴

3.4. Results

The Postel method described in this paper links 7,345 Chinese individuals between 1880 and 1900. A three-fold increase over baseline, these gains were driven mostly by segmentation and name order changes (accounting for 45.2% and 44.5% of new matches, respectively). Character standardization contributed the remaining 10.3%. I link 9.6% of the 1900 Chinese immigrant population, on par with match rates for European immigrant groups.

I identify nearly three times as many matches as the ABE exact standard approach for 1880-1900 (2,721 or 3.6%). The IPUMS Multigenerational Longitudinal Panel (MLP) links less than one tenth of one percent of individuals (just 46) between these years.

Table 4 compares the observable characteristics of matched individuals with the overall population mean for each year. The Postel method and the ABE standard approach yield similarly representative samples, though both demonstrate some bias compared to the overall Chinese population particularly in terms of age.¹⁵ As with other linked data, projects using this matching approach should both discuss the sample’s representativeness and attempt to reweight the sample based on observed characteristics (Abramitzky et al. 2021).

Table 4:

Balance Test of Total Population vs Matched Observations, 1880-1900

	1880 pop.	1880 Postel	1880 ABE	1900 pop.	1900 Postel	1900 ABE
Age	31.8 (10.7)	−4.45 (0.11)	−4.59 (0.16)	41.9 (10.8)	6.3 (0.11)	5.9 (0.17)
Single (i.)	0.69 (0.46)	0.05 (0.01)	0.06 (0.01)	0.58 (0.49)	−0.02 (0.01)	−0.06 (0.01)
Literate (i.)	0.77 (0.42)	0.03 (0.01)	0.01 (0.01)	0.72 (0.45)	−0.04 (0.01)	−0.03 (0.01)
Socioeconomic Index	13.7 (13.4)	0.85 (0.16)	1.01 (0.25)	16.3 (17.6)	−1.69 (0.20)	−1.32 (0.33)
Lives in CA (i.)	0.70 (0.46)	−0.04 (0.01)	−0.01 (0.01)	0.50 (0.50)	0.09 (0.01)	0.04 (0.01)

Notes. The columns marked “pop” correspond to the population mean and standard deviation of all observations for the specified year. An ”i.” designates an indicator variable; reported figures correspond to the share of the population with that characteristic. The table presents the balance test between my approach and the ABE standard algorithm. Estimates correspond to the difference in averages between the total and matched observations for a given algorithm and are reported in the first line; standard errors are reported in parentheses in the corresponding second line.

4. Robustness and Accuracy

This section conducts a robustness exercise, applying the approach detailed above to another census year pair (1900-1910). I also compare the quantity, accuracy, and uniqueness of my links to those produced by ABE, MLP, and BYU Census Tree.¹⁶

4.1. Quantity

Table 5 below shows that the Postel method matches 7,272 individuals from 1900 to 1910 (9.5% of the 1900 population). This result is second only to the BYU Census Tree, which links 12,855 individuals in this year pair. The Census Tree can be considered an upper-bound estimate of a semi-automated approach, given the volume of their individually validated training data (Price et al. 2021). Both ABE and MLP demonstrate higher match rates than for 1880-1900, but are still significantly outstripped by the method proposed in this paper.

Table 5:

Match rate comparisons

	1880-1900	1900-1910
Postel	7,345 (9.6%)	7,272 (9.5%)
ABE	2,721 (3.6%)	5,566 (7.3%)
MLP	46 (0.06%)	2,160 (2.8%)
Census Tree	—	12,855 (16.8%)

4.2. Accuracy

The prior section demonstrates how this approach increases the quantity of successful links. What – if anything – can we say about link quality? Unfortunately, the lack of “ground truth” data for the time period and demographic group under consideration precludes any systematic assessment of the accuracy of Postel method links.¹⁷

However, a manual validation exercise conducted on a random sample of links is illustrative. 200 matches from each linkage approach were randomly selected and reviewed for accuracy. Table 6 below reports the results of this exercise.

Table 6:

Match accuracy (1900-1910)

	Postel	ABE	MLP	CT
Exact	41 (20.5%)	54 (27.0%)	24 (12.0%)	25 (12.5%)
Likely	42 (21.0%)	48 (24.0%)	19 (9.5%)	32 (16.0%)
Plausible	117 (58.5%)	59 (29.5%)	62 (31.0%)	73 (36.5%)
Implausible	0 (0.0%)	39 (19.5%)	95 (47.5%)	70 (35.0%)

An “exact match” means both names and ages are identical between the two years. A “likely” match consists of individuals with identical names and ages one year apart (e.g. if an individual is 42 years old in 1900 and 51 or 53 in 1910 with exact name correspondence they are considered a likely match). I consider a match “plausible” if individuals either have 1) identical names and ages two years apart or 2) similar – but not identical – names with ages one year apart. Finally, “implausible matches” are matched individuals whose ages are more than three years apart or have very different names.¹⁸

This exercise demonstrates that Postel matches are of higher quality than those produced by other algorithms. This improvement is almost entirely due to eliminating “implausible” matches through language-specific name pre-processing.¹⁹ The matches produced by ABE are of next highest quality, likely due the “exact” approach requiring exact name matches (i.e. no name standardization) and limiting age discrepancies to a five-year band. In contrast, the MLP and Census Tree algorithms yielded both the fewest “exact” matches and the most “implausible” matches. Likely due to these algorithms’ flexibility, a high share of the randomly sampled matches suffered from large age differentials and extremely different names.

These differences in match quality are reflected in a balance test for 1900-1910 (see Appendix Table A1). The Postel and ABE methods generally yield more representative samples than Census Tree or MLP links.

4.3. Uniqueness

Inspecting match uniqueness further underscores the Postel method’s similarities and differences from other algorithms. As seen in Table 7 below, this paper’s approach identifies 2860 matched pairs not linked by any other algorithm. The remaining 60.7% of matches are found by at least one other matching algorithm.

Table 7:

Uniqueness of Postel matches, 1900-1910

	Matched pairs (% of total)
Unique	2860 (39.3%)
Shared with one other	2303 (31.7%)
ABE 20	1313
MLP	71
CT	919
Shared with two others	1768 (24.3%)
ABE+MLP	99
ABE+CT	1584
MLP+CT	85
Found by all	341 (4.7%)
Total Postel	7272

Of the matches unique to this approach, 680 stem from the baseline match, 291 from the segmentation step, 1525 from the name order step, and 364 from standardization. Only the Postel method reverses the name order of potential matches so it makes sense this step accounts for the largest number of unique matches. This comparison also highlights the importance of language-specific name cleaning procedures, given that my baseline match diverges from the other methods mainly by avoiding erroneous adjustment by phonetic or string-distance algorithms.

5. Conclusion

This project develops an approach to remedy low record linkage rates for Chinese immigrants in the 19^th- and 20^th-century United States. The ability to track members of the first major non-white immigrant group in the United States across time enables insights into core sociopolitical processes like racial boundary formation, immigrant integration, and immigration policy effectiveness. This approach triples the number of matches compared to baseline, bringing Chinese match rates in line with that of some European immigrant groups. Both the quantity and the quality of these matches are higher compared to standard record linkage approaches.

This approach could also be used to match Chinese women, as the convention of changing one’s surname is not present in Chinese.²¹ This was a small population but substantively important to understand gender-based immigration restrictions. Additionally, a similar approach could be tailored for other East Asian immigrant groups with character-based languages (e.g. Japanese).

More broadly, the procedures developed in this paper indicate the importance of group-specific name pre-processing for record linkage. Given relatively low match rates for immigrant groups, using linguistically-tailored matching approaches offers an important opportunity to study minority group experiences and reduce bias in overall linked samples.

A. Appendix

A.1. Commonly Used Terms

• “First name” and “last name” refer to an individual’s name as enumerated in the indexed census database (i.e. IPUMS full-count datasets).

• “Surname” and“personal name” refer to an individual’s “real” name in Chinese. As discussed above, an individual’s true surname could have been recorded in either the “first name” or “last name” columns of the indexed census data.

• “Name fragments” refer to each individual part (typically single character) of a name.

• “Indexed” or “transcribed” refers to the computer-readable database (e.g. IPUMS full-count census data) while “enumerated” refers to the underlying census forms (hand-written).

• A “crosswalk” is a file mapping equivalent elements across two or more distinct datasets.

A.2. Identifying character equivalents in the New York Exclusion File database

Surname characters in the New York Exclusion database were identified with four-corner codes, a now mostly obsolete codification scheme to numerically encode characters. Validating and refining the list of four-corner codes yields a crosswalk of 413 Romanizations mapped to 152 unique character equivalents. Four-corner codes narrow the possible character set immensely, but they are not always a unique character identifier.

To ensure I choose the correct character equivalent, I validate each four-corner code in the MBDG online dictionary. I choose the relevant character based on whether its definition indicates use as a surname. If the MDBG definitions do not indicate surname use, I search the genealogical website My China Roots using the Romanized spelling in the New York database and compare potential options with those offered by the MDBG four-corner code search. I leave the entry blank if no character equivalent is found. I further refine the possible character set by expanding the four-corner code by one digit. For example, the four-corner code 8211 produces eleven possible character matches. Specifying code 8211.4 narrows the choice set to two characters, only one of which is designated as a surname.

Table A1:

Balance Test of Total Population vs Matched Observations, 1900-1910

	1900 pop.	Postel	ABE (std)	MLP	CT	1910 pop.	Postel	ABE (std)	MLP	CT
Age	41.9 (10.8)	−3.21 (0.18)	−2.86 (0.13)	−2.16 (0.20)	−3.21 (0.09)	44.9 (12.9)	4.66 (0.12)	4.30 (0.15)	5.33 (0.19)	5.52 (0.11)
Single (i.)	0.58 (0.49)	0.04 (0.01)	−0.01 (0.01)	−0.09 (0.01)	0.07 (0.01)	0.55 (0.50)	−0.05 (0.01)	−0.07 (0.01)	−0.11 (0.01)	−0.05 (0.01)
Speaks English (i.)	0.62 (0.48)	0.02 (0.01)	0.01 (0.01)	−0.04 (0.01)	0.01 (0.01)	0.56 (0.50)	0.03 (0.01)	0.02 (0.01)	−0.05 (0.01)	0.02 (0.01)
Literate (i.)	0.72 (0.45)	0.02 (0.01)	0.03 (0.01)	0.06 (0.01)	0.03 (0.004)	0.82 (0.39)	−0.02 (0.01)	−0.02 (0.01)	0.06 (0.07)	−0.02 (0.004)
Socioeconomic Index	16.3 (17.6)	0.01 (0.21)	0.92 (0.25)	4.38 (0.47)	0.95 (0.17)	21.2 (22.3)	0.30 (0.28)	1.28 (0.34)	3.52 (0.54)	1.17 (0.23)
Immigration Year	1879.1 (8.6)	1.29 (0.10)	1.13 (0.11)	1.24 (0.16)	1.55 (0.08)	1886.8 (11.8)	−3.78 (0.13)	−3.52 (0.15)	−5.13 (0.20)	−4.21 (0.11)
Lives in CA (i.)	0.50 (0.50)	−0.02 (0.01)	−0.01 (0.01)	0.11 (0.01)	0.01 (0.01)	0.50 (0.50)	0.04 (0.01)	0.02 (0.01)	0.13 (0.01)	0.03 (0.01)

Notes. The columns marked “pop.” correspond to the population mean and standard deviation of all observations for the specified year. An ”i.” designates an indicator variable; reported figures correspond to the share of the population with that characteristic. The table presents the balance test between my approach and three other standard matching algorithms. Estimates correspond to the difference in averages between the total and matched observations for a given algorithm and are reported in the first line; standard errors are reported in parentheses in the corresponding second line.