## Abstract

Interstate elderly migration has strong implications for state tax policies and health care systems, yet little is known about how it has changed in the twenty-first century. Its relative rarity requires a large data set with which to construct reliable measures, and the replacement of the U.S. Census long form (CLF) with the American Community Survey (ACS) has made such updates difficult. Two commonly used alternative migration data sources—the Current Population Survey (CPS) and the Statistics of Income (SOI) program of the Internal Revenue Service (IRS)—suffer serious limitations in studying the migration of any subpopulation, including the elderly. Our study informs migration research in the post-2000 era by identifying methodological differences between data sources and devising strategies for reconciling the CLF and ACS. Our investigation focusing on the elderly suggests that the ACS can generate comparable migration data that reveal a continuation of previously identified geographic patterns as well as changes unique to the 2000s. However, its changed definition of residence and survey timing leaves us unable to construct a comparable national migration rate, suggesting that one must use national trends in the smaller CPS to investigate whether elderly migration has increased or decreased in the twenty-first century.

## Introduction

The growing size and potential impact of the elderly population in the United States has made that group a target of state-level policy makers, who argue that income tax breaks and estate tax reductions are necessary to prevent them from moving out of state to other states with more desirable tax policies, such as Florida and Texas, which have neither tax. These actions suggest that policy makers, at least, believe that the elderly are mobile—perhaps increasingly so. Elderly migration has long been studied (for reviews, see Bradley and Longino 2009; Uhlenberg 2006; Walters 2002), and each decennial U.S. census has brought new research investigating who is moving where (Bean et al. 1994; Conway and Rork 2010; Flynn et al. 1985; Lin 1999; Longino and Bradley 2003). However, no update on interstate elderly migration patterns has occurred since the replacement of the U.S. Census long form (CLF) with the American Community Survey (ACS).

Investigating the relatively rare event of elderly interstate migration requires a large sample, which explains why researchers have relied heavily on CLF data.1 This reliance also highlights the critical need to find a way to use and make comparable the largest sample available for the twenty-first century: the ACS. Using the ACS and comparing it with the CLF presents many choices and challenges (Franklin and Plane 2006; Newbold 2011; Rogers et al. 2003), several of which are especially acute when studying the elderly.

In this research, we first identify the challenges in obtaining comparable migration measures, and then we use a variety of empirical techniques and data sets to implement and measure the success of our proposed solutions. Although our focus is the elderly, this research is applicable to other key subpopulations, such as potential welfare recipients or recent college graduates, for whom alternative data sources are also likely inadequate. We conclude with evidence as to how elderly interstate migration has changed, and we offer recommendations for using these data sources to study migration more generally.

## Migration Data and Measures

Our primary sources are public use microdata samples from the 1980, 1990, and 2000 CLF and the 2006–2010 ACS. We also use data from the Current Population Survey (CPS) and the Statistics of Income (SOI) program of the Internal Revenue Service (IRS). Because all four sources measure migration by comparing current with past residence, they identify migrants rather than moves. Table 1 describes key characteristics of each source and reports key measures for the elderly (age 65+) and the overall population.2

The CLF public-use, individual-level data represent approximately 5 % of the U.S. population and have been used extensively in past research (e.g., Conway and Rork 2010, 2012; Flynn et al. 1985; Lin 1999; Longino and Bradley 2003). On census day, April 1, the CLF asked respondents to compare their current usual residence—“… the place where a person spends ‘most’ of his or her time” (Van Auken et al. 2006:278)—with where they resided five years ago, thereby capturing migration over five-year periods.

The CLF ended in 2000 and was replaced with the ACS, which became nationally representative in 2005. Like the CLF, the ACS is a mandatory survey conducted by mail, telephone, and personal interviews. The ACS is conducted annually, with continuous sampling throughout the year, and its publicly available, individual-level data are based on 1 % of the U.S. population. (See Table 1.) Therefore, five years of ACS data are required to approximate the CLF sample size. The ACS migration question compares current residence with that one year ago, thus capturing migration over a one-year period. Because of the smaller sample size and shorter migration window, in most analyses, we use 2006–2010 ACS data (capturing 2005–2010 migration) to create a comparable counterpart and what we dub a 2010 update to the earlier CLF samples.

The CPS and the SOI are the other most commonly used sources. Both are ongoing and contain migration measures over a one-year period; the CPS contains five-year migration measures for some years. However, both data sets suffer severe limitations, as revealed in Table 1. For example, the CPS is a voluntary survey, conducted by telephone and in-person interview, with much more limited follow-up than the ACS or CLF, which therefore leads the CPS to find fewer migrants than the other data sources (Kaplan and Schulhofer-Wohl 2012:1071). The CPS’s small sample size constrains its ability to detect geographic patterns or the migration behavior of small or relatively immobile populations, such as the elderly. Although the population at risk (in this case, those aged 65 or older) is approximately the same proportion in the CPS (at 10 % to 15 %) as in the ACS or CLF, its much smaller sample size yields dramatically fewer at-risk observations; for example, elderly observations range from 15,530 to 22,507 in the CPS versus 0.6 to 1.85 million in the CLF. Likewise, Table 1 reveals that although the migration rates are similar across the data sources, these low rates yield a very small number of migrants in the CPS (<275). The standard error of the migration rate, which is inversely related to sample size, illustrates this shortcoming. The ACS (one-year) and CLF (five-year) each yield standard errors in the range of 0.015 %, whereas the CPS yields standard errors more than four times as large (0.065 % for one-year measures and 0.13 % for five-year measures). These standard errors are large relative to the low rate of migration (~1 % for one-year measures and ~4 % for five-year measures), which hinders the detection of statistically significant changes over time. The same issue holds for the general population, although its larger sample sizes and migration rates make the problem less acute.3

The SOI is based on counts of taxpayers (i.e., exemptions) and where their tax returns are filed. Only total counts are provided, and these taxpayer counts cannot be broken down into demographic groups. The SOI data also miss those who are not required to file federal income tax returns and thus “under-represents the poor and the elderly” (Gross 2014:2). Likewise, the SOI data miss taxpayers who file late, who tend to have the more complicated returns of high-income households and thus “may under-represent the wealthy as well” (Gross 2014:2). The CPS and SOI data are thus quite limited for studying the migration of subpopulations, including the elderly. Nonetheless, because they span the 1980–2010 period, they prove useful in bridging the gap between the ACS and CLF.

Three migration measures are analyzed. First, the national migration rate, Mt, is the number of elderly individuals moving to another state during the migration interval (or reference period) ending in year t (e.g., 1995–2000) divided by the population at risk—that is, the elderly population in the first year (e.g., 1995). This measure has been used in studies of the possible decline in migration (Kaplan and Schulhofer-Wohl 2012; Molloy et al. 2011; Wolf and Longino 2005). We estimate the following:
$Mkt=α+βtimekt+θIkt+εkt,$
1
where k denotes data source, time is a time trend, and I is a dummy variable denoting source k. These regressions facilitate comparisons by adjusting for the different years observed and yield estimates of the long-term time trend (β) and persistent differences across sources (θ).

Second, the state migration rate, Rit, is the number of state i elderly migrants divided by the state elderly population. Three possible rates exist: (1) in-migration rate, (2) out-migration rate, and (3) net in-migration rate (in-migrants minus out-migrants). We focus on the net in-migration rate because it best summarizes the geographic patterns of migration and their implications for state population growth.4

Third, state-to-state migration flows, Fijt, are the number of elderly moving from state i to state j by time t. State-to-state migration flows are the most detailed aggregate measure of interstate migration available, and the log of these flows serves as the dependent variable in standard gravity models. Because there are 51 × 50 = 2,550 flows per year, we report only the top 30 flows; to measure how concentrated elderly migration is, we measure the percentage of total migrants accounted for by these top flows.5 Net flows are Fijt– Fjit.

We then compare the rates and flows across the four years (1980–2010) with rankings and correlation coefficients.

## Challenges and Solutions

The unique features of the CLF and ACS create four challenges.

1. Small sample sizes. Given the historically low rate of interstate elderly migration (~1 % per year), a very large data set is required to observe a substantial number of migrants. Although the size of the ACS over five years is comparable with that of the CLF, its shorter migration interval results in far fewer observed migrants. This smaller number of migrant observations in the ACS versus the CLF, evident in Table 1, leads to greater irregularities in migration measures (e.g., Raymer and Rogers 2007). We therefore caution against using the ACS to make inferences about annual changes in elderly migration patterns and instead emphasize results using 2006–2010 data.

2. Incomparable age groups. Typical CLF elderly migration measures are constructed by limiting the sample to those aged 65 or older at the time of the census, thus capturing migration taking place up to five years before, when respondents were as young as age 60. What, then, is the comparable age cutoff for the ACS? Because mobility is relatively high for the younger elderly (Sergeant et al. 2008), their migration behavior matters. We thus propose using a multi-age approach (MAA). The first year (2006) includes those over age 61, which captures moves by anyone over age 60 in 2005–2006. The second year (2007) includes those over age 62, thereby capturing moves by those over age 61 in 2006–2007. Similarly, we limit the sample to those aged 63 or older in 2008, 64 or older in 2009, and 65 or older in 2010. This problem and our proposed solution are applicable whenever a specific age group is studied.

3. One-year versus five-year measures. Converting one-year rates into five-year rates is not as simple as multiplying the former by 5 because of the potential for multiple moves for individuals and because of possible survivor bias.6 To our knowledge, no agreed-upon adjustment exists for either the general population or specific subgroups. We take an approach similar to that of Rogers et al. (2003), using historical data on one-year and five-year migration rates to calculate a range of conversion factors. The CPS provides one-year measures for every year except for 1985, as well as five-year measures for 1985, 1995, and 2005. We calculate conversion factors as the ratio of the five-year rate to the average of the one-year rates during the same five-year period.

4. Different residence definitions. Perhaps the biggest challenge is the changed definition of residence in the ACS. The CLF, CPS, and SOI all use a “usual” or de jure (National Research Council 2006) residence measure and occur in the spring. By contrast, the ACS defines current residence as where one now resides and has lived—or will live—for at least two months, which is an actual or de facto measure; the ACS also samples throughout the year, rather than solely in spring. The ACS therefore more likely captures seasonal residents because of its de facto definition (Van Auken et al. 2006) and because it surveys people during periods of extended stays (e.g., winter for “snowbirds”). The respondent is then asked, “Where did this person live 1 year ago?”; the response to this question is used to infer migration.

If respondents use the same definition of residence for one year ago, the effect on migration measures is likely small and arises mostly from changes in seasonal migration. For example, a couple who regularly move to spend the winter in Florida will not count as migrants; the couple lived in the same place one year ago regardless of when they are surveyed. Conversely, if the couple just began—or stopped—wintering in Florida, then they could count as migrants if surveyed during the winter. Like the shortened interval, the changed residence definition and continuous sampling therefore inflates the migration rate. Because the elderly are among those most likely to be seasonal migrants, this issue is especially problematic.

The CPS spans the entire period covered by the CLF and ACS. However, Kaplan and Schulhofer-Wohl (2012) showed that the CPS migration rates were falsely inflated during 1999–2005, when census imputation methods were briefly changed. Finding a similar pattern, we follow their recommendation and omit imputed observations from our analyses. Estimating Eq. (1) for the ACS and CPS one-year rates when both exist (2006–2010) and, similarly, for the CLF and CPS five-year rates during 1980–2000 provides estimates of the inflation (θ) and the adjustments necessary to make the ACS and CLF rates comparable.

These last two challenges may also affect the geographic pattern of migration (the rates and flows) because some states experience more repeat and seasonal migration than others (e.g., Florida). Because the proposed adjustments are scalar multiplications, they do not affect the geographic rankings and correlations. Instead, we offer that net migration measures are likely to be less affected than gross measures because the repeat/seasonal migrants cancel out, on average. The individual who moves from New York (NY) to Florida (FL) and back within a five-year period is both an out-migrant and an in-migrant, and thus has no effect on the number of net migrants to New York or on the net NY–FL flow. We therefore expect to see stronger similarity between the ACS and CLF for net measures than gross ones.

## Findings

Figure 1 reports national migration rates from the CPS, CLF, and ACS in each available year. All four series slope slightly downward, suggesting a modest downward trend in migration. Comparing the five-year rates from the CLF with the CPS (top two lines) and one-year rates from the ACS with the CPS (bottom two lines) reveals that both the CLF and the ACS yield higher rates than the CPS. These tendencies have been documented for the general population; Molloy et al. (2011) documented the downward trend in migration rates for the general and working populations, and Kaplan and Schulhofer-Wohl (2012) noted that the ACS has higher migration rates than the CPS because of differences in survey procedures.

Estimating Eq. (1) for the CLF and CPS five-year rates during 1980–2005 yields Eq. (2):
$Mkt=3.541−0.0348×time+0.8491×CLFdummyvariable,57.79–2.6218.74$
2
with t statistics listed in parentheses. These results confirm these two tendencies, suggesting a decline of 0.0348 over each five-year period (less than a 1 % change) and revealing that the CLF rates are substantially higher (by approximately 25 %) than the CPS rates. The same regression estimated for the bottom two lines, the ACS and CPS one-year rates during 2006–2010, yields Eq. (3):
$Mkt=0.6876−0.0564×time+0.5753×ACSdummyvariable,12.15–3.6018.74$
3

These results suggest a much steeper decline in migration—an almost 10 % decline per year—which is clearly evident in Fig. 1. They also reveal that the ACS rates are proportionately much higher than the CPS rates and thus are inflated, even relative to the CLF, substantiating that the ACS’s continuous sampling and actual residence definition inflate migration in the ACS relative to census data.

The dashed lines in Fig. 1 show the 2006–2010 five-year migration rate predicted by the ACS, first using the five-year/one-year conversion factor (●) and then also adjusting for inflation (▲). Applying a five-year/one-year conversion factor of 3.325 to the MAA rate of 1.30 results in a 2006–2010 five-year rate of 4.33—a slight increase over 2000. However, our calculations suggest that ACS migration rates are inflated by approximately 50 % over the CLF; this adjustment reduces the five-year rate to 2.88—a dramatic decline.7 These exercises reveal the difficulty in creating a comparable ACS national migration rate.

To draw a conclusion about long-run trends, we instead use the CPS; even with its small sample size and associated large standard errors, the CPS yields statistically significantly lower rates of migration in the late 2000s than in past decades. Although very few changes in adjacent years are statistically significant from 0, the migration rates in the late 2000s are statistically lower than almost all earlier years. Moving back in time, however, far fewer differences are statistically significant—a further indication of the limitations imposed by the CPS’s small sample size. Nonetheless, these exercises along with the regression results from Eqs. (1) and (2) point to a decline in elderly migration in the 2000s.

Fortunately, the ACS appears more comparable in its geographic patterns, especially if the MAA and net measures are used. Tables 2 and 3 report the net migration rates and top 30 flows from the three censuses and the 2006–2010 ACS. These tables offer support for our MAA approach. The last two sets of columns in Tables 2 and 3 show that the MAA measures correspond more closely to the CLF than the 65+ measures. They yield fewer arrows (which denote a change of 10+ spots since 2000) in Table 2 and fewer zero flows (bottom line of Table 3).

Table 4 formalizes these comparisons with correlation matrices for each measure across years for the CLF/ACS and, for comparison, the SOI data, which is consistently measured throughout the period. Comparing the numbers above and below the dashed lines shows that the 2010 MAA measures are almost always more highly correlated with the 1980, 1990, and 2000 CLF measures than are the 2010 measures for those aged 65 or older.

The correlations reported in Table 4 also provide support for our assertion that using net measures rather than gross measures improves the comparability of the CLF and ACS. The over-time correlations between the CLF and the ACS for the gross measures (in-migration, out-migration, and gross flows) reveal a dramatic decline in 2010. For example, the correlation between the in-migration rate in adjacent census years is 0.978 for 1980 versus 1990 and 0.975 for 1990 versus 2000, compared with 0.894 for 2000 versus 2010. Immediately below these matrices are the correlations for the SOI data, which do not show this dropoff. However, repeating these exercises for net in-migration and net flows, reported on the right side of Table 4, shows more similarity between the data sources over time. Both the CLF/ACS and the SOI data suggest that net migration changed more in 2010 than in preceding years, and the decline in correlations for 2010 is quite similar across the sources.

Thus, the changes that we see in the ACS net measures seem likely to be capturing genuine changes since 2000. As shown in Tables 2 and 3, some changes are continuations of past trends, such as the decline of Florida and the ascent of the Carolinas and Idaho as destinations. These trends are consistent with the steadily declining concentration of elderly migration shown in Table 3, in which 35 % of flows were accounted for by the top 30 in 1980, compared with only 23 % in 2010.8 Changes unique to the 2000s include the decline of Nevada, Louisiana, and Virginia as destinations. The first two are plausible given the housing crisis and Hurricane Katrina, respectively; declines in all three states also appear in the SOI data.

## Conclusion

Methodological differences between the ACS and CLF make constructing comparable migration measures difficult. The remedies proposed here lead to reasonably comparable measures of net state-level migration rates and flows that identify several credible changes in the geographic patterns of elderly migration since 2000. This is good news for researchers investigating the determinants of migration patterns, such as state-level policies, over time. For those interested in long-run national trends in migration, however, the ACS appears unable to yield a national migration rate that is comparable with historical rates. Despite its small sample size (and thus large standard errors), the CPS is the best option for long-run trends and strongly suggests that migration of the elderly, like that of other groups, has declined in the twenty-first century.

## Acknowledgments

We thank the Editors, referees, and participants in our session at the Population Association of America annual meetings for their helpful comments.

## Notes

1

Ruggles (2013:293) touted the importance of such data as well; while offering advances for migration researchers, the discontinuity in U.S. data caused by the switch to the ACS was not discussed. Similarly, the problems caused by this discontinuity are not addressed in recent work that combines the two sources to study patterns over time (e.g., Iceland et al. 2012).

2

See also https://www.census.gov/hhes/www/poverty/about/datasources/factsheet.html for a comparison of the survey methodology and population universe of the CPS and ACS, and Willekens (2016) for a more general discussion of the challenges and issues in measuring migration.

3

The standard error formula is $p1−p/n$, where p is the proportion who migrate, and n is the sample size. Across all data sources, the standard error for the total population is approximately one-half the size of the elderly’s, whereas the migration rate (p) is more than twice as large. The full set of calculations is available upon request.

4

Willekens (2016) pointed out that the population at risk is difficult to define for a net migration rate because the rate captures those moving into the state from other places. Still, one must adjust for population size, and this approach is common.

5

This measure is similar to that reported by past over-time comparisons and updates of elderly migration (e.g., Flynn et al. 1985; Longino and Bradley 2003) except that they focus on in-migrants and out-migrants separately rather than flows. See also Rogers and Raymer (1998), who discussed alternative measures of spatial focus and recommend the coefficient of variation (CV). Results based on the CV confirm our conclusion regarding concentration.

6

During any given time interval, individuals can move multiple times such that the number of moves exceeds the observed number of migrants. A longer interval also increases survivor bias because individuals must survive to an older age to be observed (e.g., age 85 vs. 81 for a move made at age 80). This bias is especially acute for the elderly. For both reasons, the number of moves and migrants missed grows with the length of the interval.

7

Details of these calculations are available upon request.

8

The CVs for each year (4.7, 3.9, 3.2, and 2.5, respectively) also show a decline in concentration.

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