Our study focuses on two populations in New York City: students and Medicaid enrollees. The New York City Department of Education (DOE), the largest school district in the United States, serves roughly one million students each year. New York City offers grades PK through 12. A substantial proportion of these students come from economically disadvantaged backgrounds; approximately 74 percent were classified as such in the 2023–24 school year [9]. We obtained enrollment records for all students attending school in New York City between the 2006–07 and 2024–25 school years with 21,078,606 total observations, representing 3,451,692 unique student IDs.

Medicaid is the largest public insurance program for low-income Americans, providing access to a wide range of medical services. Medicaid enrollment records were obtained from the Salient New York State Medicaid Enterprise System (NYSMES) and include all enrollments for individuals residing in New York City from January 2006 through June 2025. For consistency with the school-aged population, we restrict the sample to children between ages 3 and 20 during the observation window totalling 23,641,337 observations representing 3,541,508 unique enrollment IDs.¹

Although there is no shared identifier across sources, both follow a highly parallel structure. Each dataset includes its own internal unique identifier, along with individuals’ first and last names, date of birth, record year, gender, race, and residential ZIP code. This close alignment in available fields allows us to construct and apply a common matching model across datasets, as discussed below.

Figure 1 presents the distribution of unique person identifiers by year of birth from 1986 to 2022 in the underlying DOE enrollment and Medicaid administrative data, before applying de-duplication or matching procedures. While the figures highlight substantial overlap across cohorts, the overall distributions differ. The DOE data follow an approximately normal distribution, as expected for administrative education records concentrated around school-aged children. In contrast, the Medicaid data exhibit a bimodal distribution, with a pronounced increase in enrollment among individuals born between 2000 and 2004. This jump likely reflects several factors including major expansions in children’s Medicaid eligibility during the early 2000s (including indirect spillover from the Children’s Health Insurance Program expansion), improvements in administrative data capture, and a policy shift from strict re-certification toward continuous eligibility for Medicaid-eligible children [10–12]. Differences in the cohort (birth year) distributions across the two datasets, together with improvements in administrative reporting over time, help explain why not all records have corresponding matches across sources.

We design a two-step linkage algorithm with the goal of creating a unique person-level link between New York City Medicaid and Department of Education (DOE) records. We follow the standard pipeline for probabilistic matching: pre-processing, blocking, and matching [13], and extend it using supervised machine learning to improve accuracy and scalability. We calculate linkage rates across race and time to evaluate the model’s performance and ensure equitable matching across demographic groups.

The first step involves de-duplication within datasets. Each dataset contains strong within-system unique identifiers, but a small share of individuals are assigned multiple identifiers due to administrative errors such as enrollment lapses, typographical mistakes, or re-enrollment under a new ID. We trained two supervised models, one for Medicaid and another for DOE, to identify and consolidate duplicate records within each dataset so that each individual is represented by a single record.

The second step focuses on cross-dataset linkage. We use the models trained in step one to evaluate candidate pairs across the Medicaid and DOE datasets. This step moves from searching for duplicates (i.e., records belonging to the same person) within a single dataset, to identifying potential matches between the two systems. Records were blocked on key identifiers to reduce computational complexity and then scored using the models to classify true matches. Creating the models that are used to eventually link the two datasets is a large reason why we do not simply de-duplicate based entirely on unique ID numbers. This gives us an advantageous situation, where ID numbers are strong enough to be used as truth labels in model training, but can be improved upon as final duplicate labels.

This staged approach improves upon deterministic and purely probabilistic methods by first addressing data quality issues within each dataset and then applying machine learning to identify cross-dataset matches. Within these two steps, our methodology consists of two sub-steps: 1) pre-processing data and 2) de-duplication. The de-duplication tasks consist of blocking the datasets to generate candidate pairs, training a supervised machine learning model, scoring candidate pairs with match probabilities, and applying clustering to group matched records. We provide a detailed description of each process in the following sections.

We start by pre-processing both datasets individually. Pre-processing ensures the data are accurate, consistent, and comparable across sources by correcting errors, standardising formats, and handling missing or duplicate information. The goal is to improve data quality so that subsequent linkage steps, such as blocking and matching, are more reliable and efficient. Both Medicaid and DOE include structured administrative records containing personal identifiers, such as name, date of birth, gender, zip code, and race. For each dataset, we conduct the following cleaning steps: 1) Separate date of birth into day, month, and year; 2) Remove leading and trailing whitespace from strings; 3) Separate name suffixes into their own variable; 4) Standardise all ZIP codes to five digits (e.g., leading zeros if necessary); 5) Remove extraneous characters from string fields, e.g. ‘3’, ‘/’, ‘,’; 6) Standardise race and gender labels²; and 7) De-duplicate exact copies. After performing these steps, we move onto de-duplication.

Once standardised through pre-processing, we proceed to de-duplication to ensure each individual is represented by a single record. This step reduces redundancy and computational complexity before cross-dataset linkage. Because de-duplication requires comparing millions of records, we use a blocking strategy to limit comparisons to records sharing key attributes such as name or date of birth, dramatically reducing runtime while retaining nearly all potential true matches.

De-duplication is necessary for several reasons. First, individuals often appear multiple times within each dataset, once per school year in the DOE data and once per month enrolled in the Medicaid data, making direct linkage computationally prohibitive and noisy. Second, unique identifiers cannot be relied upon exclusively: individuals may reenter these systems and occasionally receive new IDs following administrative updates. Finally, because our broader goal is to develop a linkage model that functions even when unique identifiers are unavailable allowing the trained model to be repurposed for linking the DOE and Medicaid data, we use probabilistic supervised learning methods to de-duplicate each dataset prior to cross-dataset linkage.

Following pre-processing, we implement the following steps for the de-duplication process: 1) Block each dataset against itself to generate candidate record pairs for comparison; 2) Train a random forest classifier to distinguish true duplicate pairs from non-matches; 3) Score each candidate pair using the trained model to assign a match probability; and 4) Apply clustering to group together records identified as duplicates.

After de-duplicating both datasets, much of the groundwork for record linkage has already been completed. Linking two datasets is conceptually similar to de-duplication: instead of linking a dataset to itself, we link the DOE and Medicaid datasets. Because of this similarity, much of the code and process developed for de-duplication, cleaning, name handling, blocking, and feature engineering, is reused with minimal modification. After blocking the DOE and Medicaid records, we generated 31,898,140 candidate pairs to consider.

Some differences arise at the model scoring stage. For each candidate pair, we use both random forest models previously trained during de-duplication (one on DOE data, one on Medicaid data) and take the average of the two match probabilities. This approach leverages the patterns learned from each dataset while maintaining consistency in feature representation.

We validated the model in two ways. First, we compared the random forest match probabilities to an unsupervised Fellegi-Sunter model, finding a correlation of r = 0.87, indicating strong agreement [22]. Second, we manually reviewed a sample of candidate pairs within decile threshold ranges signifying high-, medium-, or low-probability matches. High-probability matches generally had exact or near-exact agreement on all fields, medium probability matches often shared similar names, and low-probability matches shared very few characteristics.

We first examine match rates by birth cohort to assess whether linkage quality varies over time. Stable match rates across cohorts would indicate consistent model performance, while systematic deviations could reflect changes in administrative coverage or data quality. The average yearly match rate is 77.6% for DOE records and 83.7% for Medicaid records.³ Across both samples, match rates remain high and broadly stable, following an arc that peaks in the early 2000s before experiencing a modest decline (Figure 5). This trajectory likely reflects two intersecting factors: the expansion of Medicaid eligibility and administrative record-keeping in the early 2000s [11, 12], and differences in the length of longitudinal observation across cohorts. Midperiod cohorts benefit from extended follow-up, increasing the number of observed records and thus the cumulative opportunities for successful linkage. In contrast, later cohorts have shorter observation windows, which mechanically reduce the probability of capturing sufficient identifying metadata for a match. Consequently, these patterns appear to be driven primarily by variation in data coverage and duration of follow-up rather than deterioration in model performance.

This interpretation is reinforced when examining match rates by the number of years an individual is observed in the data (Figure 6). Match rates increase substantially with longer observation histories. In Medicaid, match rates rise steeply from approximately 25% among individuals observed for a single year to roughly 80% by five years of enrollment, after which they plateau. DOE records begin at a higher baseline (approximately 55% with one year observed) and increase steadily with additional years. These patterns underscore that linkage success improves with repeated administrative observations, consistent with the cohort-level trends described above.

Finally, the low match rates for the earliest birth cohorts (1985–1986) are mechanical. DOE enrollment records begin in the 2006–07 school year, meaning individuals born in these years would have been beyond typical school age when the data start. As a result, only those who were retained or receiving special education services would appear in the DOE records, leading to limited coverage and mechanically lower Medicaid match rates for these cohorts.

Next, we examine whether linkage performance varies across the attributes used in the matching process—race, gender, residential borough, and attribute missingness—and assess whether differences in match rates can be explained by variation in sample composition.⁴ Table 1 highlights that the DOE and Medicaid samples represent meaningfully different populations. While both datasets are roughly evenly split by gender, the DOE sample includes a higher share of Asian, Black, and White children, whereas the Medicaid sample includes a larger proportion of multi-racial children and records with missing race. Children in the Medicaid sample are also more likely to reside in Brooklyn and the Bronx, boroughs that are, on average, lower-income than the rest of New York City.

Overall, missingness in the variables used for linkage is low. In both datasets, first name, last name, date of birth, and gender are fully observed. Race is missing for 0.4% of DOE records and 4.5% of Medicaid records, while residential borough is missing for approximately 4% of DOE records and 2.5% of Medicaid records. Consistent with expectations, records missing information used in the linkage process are less likely to match, and match rates among records with missing race or borough exhibit greater variation over time.

Match rates vary substantially across racial groups and are strongly related to representation in the underlying data. In both the DOE and Medicaid samples, White children and children with missing race information have noticeably lower match rates than other groups. We fit separate logistic regression models to estimate the association between each demographic characteristic (race, gender, and residential borough) and the probability of matching, controlling for the remaining two characteristics in each model. The results are presented as adjusted odds ratios with 99% confidence intervals. Our results indicate that, relative to White children, Asian, Black, Hispanic, and Native American children are between four and eight times more likely to successfully match (Table 2). These differences persist across datasets, suggesting that lower match rates among White children are not driven by a single data source but instead may reflect systematic differences in name commonality or population representation. In contrast, match performance does not differ meaningfully by gender: males and females are equally likely to be matched in both datasets (Table 2). Differences by residential borough are more pronounced. The Bronx consistently exhibits the highest match rates in both the DOE and Medicaid samples. In the DOE data, however, match rates vary more widely across boroughs, with Staten Island exhibiting the lowest match rate, approximately 61%. Staten Island is one of the wealthier boroughs in New York City and is less represented in the Medicaid sample, which may limit the availability of high quality candidate matches.

Taken together, these results suggest that differences in linkage performance are driven less by demographic characteristics themselves and more by differences in population coverage, name commonality, and sample overlap across data sources. Because New York City is highly diverse and naming conventions vary across linguistic and cultural contexts, name-based similarity measures—including phonetic encodings, string similarity, and embedding-based features—may perform differently across groups. Importantly, match rates are broadly stable over time within racial groups, indicating that the combined feature set is temporally robust, even if performance is weaker for groups with more common names or lower representation across linked datasets (Figures 7, 8).

Several mechanisms are consistent with the lower match rates observed for certain subgroups. First, records with missing information are mechanically more difficult to link because the algorithm has fewer attributes on which to establish similarity. Even small amounts of missingness can reduce the probability of identifying a high confidence match, particularly in large administrative datasets where many individuals share similar names or dates of birth.

Second, differences in match rates may reflect differential representation across the two data sources. Children from higher-income households are less likely to be enrolled in Medicaid, which mechanically limits the pool of potential matches regardless of linkage quality. As a result, lower match rates for groups that are disproportionately higher-income may reflect true population non-overlap between the DOE and Medicaid data rather than algorithmic failure.

As a concrete example, consider the pattern observed for White children where match rates for White children are approximately 50% in both the DOE and Medicaid samples. If lower match rates were driven solely by under-representation in Medicaid, one would expect lower match rates in the DOE data but comparatively higher match rates within the Medicaid sample, where Medicaid-eligible White children should still be linkable to DOE records. The similarity in match rates across data sources suggests two non-mutually exclusive interpretations. One possibility is differential institutional coverage. Medicaid-eligible White children may be less likely to appear in DOE administrative records, for example, due to private schooling or other alternative educational arrangements, while White children enrolled in DOE records may be less likely to qualify for Medicaid. A second, non-mutually exclusive possibility is reduced model performance for more common names, where higher name frequency increases ambiguity in name-based similarity measures. While the current analysis cannot distinguish between these explanations, the symmetry in match rates across data sources points to differential population overlap as an important factor shaping observed linkage performance.

Matches were evaluated based on their predicted match probabilities from the random forest model. Quantitative assessment of linkage accuracy relies on the cross-dataset validation described in Section 2dii, in which dataset-specific identifiers provide ground truth for record pairs. The manual inspection described here serves a complementary and distinct purpose. Rather than estimating error rates, it characterises the types of discrepancy present at each level of the probability distribution, so that model scores can be interpreted substantively and an appropriate acceptance threshold can be identified for our setting. The inspected samples are necessarily small relative to the scale of the linkage; they are intended to make the score interpretable, not to quantify accuracy.

Matched pairs were first stratified into equal-count deciles and a random sample of 50 pairs was inspected within each. Because the distribution of match probabilities is heavily skewed toward 1 (Figure 2), all ten deciles fell within a narrow high-probability range, and even the lowest contained only minor discrepancies such as an unmatched middle initial or a hyphenated surname truncated in one system. We therefore repeated the exercise using ten fixed-width bands of width 0.1, which span the full probability range and allow the transition from confident to uncertain matches to be observed directly.

Across bands, discrepancy patterns vary systematically. Pairs above 0.9 agree almost exactly, differing at most by a single character, a compound surname, or an additional middle initial; no sampled pair in these bands was judged incorrect. Between 0.6 and 0.8, pairs typically share at least part of the surname, a nickname or spelling variant of the given name, and one auxiliary field that is missing or discrepant. This variation is consistent with informal name recording and with fields that change over time. Near 0.4, agreement remains substantial but uncertainty increases: given names may be unrelated nicknames, and some pairs agree on given name, date of birth, race, and ZIP code while differing entirely on surname. Where the given name is common, such pairs are plausibly distinct individuals. The distinguishing feature of lower probability pairs is not the accumulation of small differences but disagreement on the individual’s name as a whole, which is the basis for our acceptance threshold. While missed duplicates cannot be quantified precisely, the one-to-one pruning step ensures that an unmatched duplicate leaves its original record correctly represented, minimising false merges.

Feature importance analysis further supports the interpreta­bility of the model: name, date of birth, and gender are the strongest predictors of true matches, with ZIP code and race contributing meaningfully, though to a lesser extent (Supplementary Appendix 4). This aligns with expectations that names, gender, and birth dates provide the most distinctive identifying information in administrative records.

Together, these analyses confirm that the linkage process performs robustly across time and population subgroups. Variations in match rates primarily reflect genuine changes in the underlying populations served by DOE and Medicaid, rather than deficiencies in the model or data quality. These results underscore the validity of the linkage and highlight the potential of integrated education–health administrative data to support future policy and research applications.

Much of the existing linkage literature treats higher match rates as evidence of better linkage quality. However, when datasets represent related but nonidentical populations, maximising coverage may increase the risk of false positives, and the appropriate benchmark is not 100% but the expected size of the population intersection. The Census Bureau’s Person Identification Validation System illustrates the upper bound: linking surveys to a near-universal administrative reference file yields Protected Identification Key assignment rates of roughly 90% for major surveys conducted since 2000 [2, 24]. When the two linked samples instead represent partially overlapping populations, the achievable rate is necessarily lower. In our context, the absence of perfect overlap between DOE and Medicaid records reflects real-world differences in eligibility and participation, not algorithmic failure. About 74% of NYC public school students are classified as economically disadvantaged each year [9]. The threshold for that classification (185% FPL) is higher than the Medicaid eligibility threshold for children in New York (154% FPL), so the share of students Medicaid-eligible each year is somewhat lower than 74%. However, kids move in and out of poverty over time, so the share ever Medicaid-eligible at some point during their childhood is higher than the single year share. With these two effects pushing in opposite directions and no NYC-specific lifetime estimate available, we surmise ∼75% is a reasonable approximation on the achievable match rate between DOE and Medicaid records. Our observed rates of 71.8% (DOE) and 70.0% (Medicaid) sit close to this ceiling and substantially exceed the 27% recovered by a deterministic match on cleaned first name, last name, date of birth, and gender.

We therefore emphasise quality over quantity focusing on whether matches are accurate, stable, and representative rather than pursuing an unattainable 100% match rate. A key feature of our approach is the use of dataset-specific unique identifiers for cross-validation: by applying a model trained on one dataset to the other—where independent identifiers provide a ground truth—we can rigorously evaluate model performance even when the underlying populations differ. This strategy allows us to maximise the information contained in each dataset while maintaining high confidence in the accuracy of identified matches.

Administrative data often contain inconsistencies such as misspellings, missing fields, or reassigned identifiers. Our feature engineering approach mitigates these challenges by incorporating multiple name-similarity measures (e.g., Jaro-Winkler, n-grams, Soundex), name-part representations, and exact demographic matches. Feature importance analysis confirms that name and date of birth variables drive model performance, while race, ZIP code, and gender play secondary roles. This structure ensures that the model remains resilient even when auxiliary demographic fields are incomplete or inconsistently recorded, an especially important property in the context of Medicaid and education data, which are collected by distinct agencies for different administrative purposes.

We explicitly frame record linkage as an exercise in uncertainty management rather than a deterministic classification task. Our high thresholds for de-duplication bias the model toward false negatives (i.e., conservatively leaving some duplicates in) while avoiding false positives that would erroneously merge distinct individuals. The clustering and pruning steps then reconcile remaining uncertainty by identifying transitive relationships among records while enforcing one-to-one pairings across systems. This multi-stage design prioritises data integrity and interpretability over computational efficiency.

To evaluate match quality, we implement stratified validation by match probability, inspecting random samples across deciles. This approach confirms that high-probability pairs reflect near-perfect administrative agreement, while lower probability pairs differ only in predictable, realistic ways such as hyphenation or middle initials. These qualitative diagnostics, combined with conventional precision, recall, and F1 metrics, provide a transparent framework for evaluating linkage quality when complete ground truth is unavailable. We separately examine coverage showing that match rates differ across racial and ethnic groups but are stable within groups over time, indicating that linkage coverage is not sensitive to administrative change.

An important caveat applies to these subgroup diagnostics. Observed differences in match rates across racial and ethnic groups are not directly interpretable as differences in linkage performance. A lower match rate for a given group may reflect genuine differences in Medicaid eligibility and enrollment, such as a smaller true population intersection, or differential model performance (for example, if name-similarity features behave less consistently for names subject to greater variation in transliteration, ordering, or hyphenation across administrative systems). Our design cannot separate these mechanisms: doing so would require a subgroup-representative sample of individuals with known enrollment status in both systems, which no available data source provides. The explanations we offer for subgroup differences should therefore be read as hypotheses for future work rather than established findings.

Our framework establishes a model for linking large-scale administrative datasets in contexts where populations partially overlap, identifiers are imperfect, and uncertainty is inherent. Rather than treating unmatched records as failures, we view them as an expected and interpretable outcome of data system boundaries. This perspective reframes linkage success in terms of accuracy, transparency, and reproducibility, offering guidance for other health, education, and policy professionals seeking to link heterogeneous administrative data sources.