new estimates of undocumented mexican migration and the probability of apprehension

Demography, Vol. 32, No.2. May 1995

New Estimates of Undocumented MexicanMigration and the Probability of Apprehension*

Douglas S. MasseyPopulation Studies CenterUniversity of Pennsylvania3718 Locust WalkPhiladelphia, PA 19104-6298

Audrey SingerPopulation Research CenterUniversity of Chicago1155 E. 60th StreetChicago, IL 60637

Using a new source of data, we estimate the probability of apprehension amongMexican migrants attempting to cross into the United States without documents. Overthe period 1965-1989 we found an average apprehension probability of .35,confirming earlier estimates. We then applied annual probabilities to estimate thegross volume of undocumented Mexican migration and adjusted these figures toderive estimates of the net undocumented inflow.

In this article we conduct three analyses relevant to current debates about the number ofMexicans migrating to the United States without documents. First, we estimate the annualprobability of apprehension experienced by Mexicans attempting to enter the countryillegally. Second, we use these figures in combination with published apprehension statisticsto estimate annual levels of gross undocumented migration between the two countries.Finally, we adjust the gross figures to account for return migration to derive annualestimates of net undocumented migration from Mexico to the United States.

Establishing the probability of apprehension accurately is important not only for whatit implies about the effectiveness of border enforcement; it also yields a means of estimatingthe flow of undocumented migrants into the United States. If one assumes that Mexicansjourney northward and attempt repeatedly to cross until they enter, then probability theorysuggests that the likelihood of apprehension is

p = RIA, (1)

where p is the probability of apprehension, A is the total number of apprehensions, and R isthe number of repeat migrants (those who have been apprehended two or more times; seeEspenshade 1990). Given the probability of apprehension, moreover, the number of grossentries (E) by undocumented Mexicans becomes

E = A(1-p)/p. (2)

* We are grateful to Robert Warren, Karen Woodrow-Lafield, Katharine Donato, and Thomas Espenshade fortheir helpful comments and suggestions on an earlier draft of this article.

Copynght © 1995 Population Association of America

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204 Demography, Vol. 32, No.2, May 1995

Thus, having an accurate estimate of the annual probability of apprehension yields a simpleadjustment factor, O-p)/p, that may be applied to published counts of Mexicansapprehended along the border to estimate the gross number of illegal Mexican entries(Espenshade 1990).

Prior work has generally estimated the odds of apprehension for Mexicans at about 1 in3 on any given attempt at border crossing (see Crane et al. 1990; Donato, Durand, andMassey 1992; Espenshade 1990; Kossoudji 1992). Using Eq. (2) and applying an assumedapprehension probability of .33 to the reported number of Mexican apprehensions in 1991yields an estimated gross inflow of 2.3 million undocumented Mexican migrants in thatyear.

Although this number is quite large, many studies show that undocumented Mexicanmigration is also characterized by a significant rate of return migration (see Durand andMassey 1992). If E represents the gross number of entries to the United States in any yearand if D is the gross number of departures, then the net number of undocumented migrants(M) may be computed as an adjustment of the gross inflow:

M = E[(E-D)/E]. (3)

Therefore, given the number of entries and departures in any year, we can compute a simpleadjustment factor, (E-D)/E, and apply it to the estimated gross inflow to yield an estimate ofnet undocumented migration to the United States.

In this article we draw on newly available data to derive independent estimates of theyearly probability of apprehension experienced by Mexicans attempting to cross the borderwithout documents. Although we derive probability estimates up to 1992, we focusattention on the period 1965 to 1990 and use the resulting annual estimates in three ways.First, we compute means for selected periods to corroborate prior empirical estimates of theapprehension probability. Second, we apply our estimated probabilities to Immigration andNaturalization Service (INS) apprehension statistics, using Eq. (2) to estimate the grossnumber of illegal Mexican migrants per year. Finally, after estimating the number of entriesand departures, we apply Eq. (3) to estimate the net inflow of undocumented Mexicanmigrants by year.

SOURCE OF DATA

Data for this analysis come from simple random samples gathered during the wintermonths of 1987-1992 in 22 communities located in the Mexican states of Jalisco,Michoacan, Guanajuato, and Nayarit; together these constitute a region that has longprovided the majority of migrants to the United States (see Jones 1988). Information aboutthe samples is summarized in Table 1; in-depth evaluations of their characteristics andrepresentativeness are available from Massey and Parrado (1994) and Massey, Goldring,and Durand (1994).

In most cases, the sample size was 200 households, but in several smaller communitieswe chose fewer cases. We constructed sampling frames by conducting a census of eachcommunity. Usually an entire town or city was canvassed, but in large urban areas, wherethis was not feasible, we demarcated and sampled specific working-class neighborhoods.Sampling fractions ranged from .029 to .699 and averaged .102. Refusals were generallynot a problem: although the rate reached 15% in one case and 11% in another, in 13 casesthe rate was under 6%. Overall it was only 6.5%.

The Mexican community data were supplemented with nonrandom samples ofout-migrants located in the United States during the summer following each winter's survey.From the community samples we determined where in the United States the migrants went

Undocumented Mexican Migration 205

Table 1. Characteristics of 22 Mexican Samples Compiled for a Study of Migration tothe United States, 1987 -1990

Mexican United States

Year Community Community

1990 of Sample Sample RefusalCommunity State Pop. Survey Size Fraction Size Fraction Rate

Metropolitan AreasLeon Guanajuato 867,920 1987 200 .232a 0 .000 .119Morelia Michoacan 492,901 1991 200 .056a 20 .096 .083Irapuato Guanajuato 362,915 1991 200 .100a 20 .999 .057Uruapan Michoacan 217,068 1992 200 .184a 13 .038 .083

Small CitiesCiudad Guzman Jalisco 74,068 1992 201 .119 20 .052 .074San Francisco Guanajuato 52,291 1987 200 .256a 20 .121 .034Salvatierra Guanajuato 33,123 1992 200 .072 15 .023 .095Los Reyes Michoacan 32,474 1989 200 .029 20 .009 .037Ameca Jalisco 30,882 1991 200 .113 20 .038 .044Yuriria Guanajuato 23,726 1992 200 .113 15 .217 .127San Felipe Guanajuato 20,614 1990 200 .053 20 .047 .047Ixtlan del Rio Nayarit 19,645 1990 200 .045 20 .012 .029Romita Guanajuato 16,535 1988 200 .073 20 .813 .057Las Varas Nayarit 11,541 1990 200 .074 20 .014 .010

TownsNahuatzen Michoacan 7,025 1990 200 .139 20 .248 .057Ario de Rayon Michoacan 6,429 1989 200 .143 20 .035 .050Union de S.A. Jalisco 4,760 1988 200 .250 20 .641 .115San Diego Jalisco 3,516 1988 200 .392 20 .127 .038

RanchosSanta Maria Jalisco 2,321 1988 200 .375 20 .260 .010La Yerbabuena Michoacan 2,240 1989 150 .335 20 .999 .152Mineral Pozos Guanajuato 1,737 1988 150 .605 10 .999 .085La Soledad Guanajuato 1,080 1991 100 .699 20 .999 .029

Total 2,284,811 1990 4,201 .102 393 .309 .065

a Sampling frameconstructed for a neighborhood within the city; all other frames cover the entirecommunity.

and sent interviewers to those areas to survey people who had settled abroad permanently.We used snowball sampling (Goodman 1961) to compile the sample of out-migrants. Inmost communities, 20 out-migrant households were interviewed, but in some cases only 10to 15 households were questioned. In Leon, Guanajuato, we were unable to include anyU.S. households because an interviewer unexpectedly dropped out of the project.

Although the snowball samples are not strictly representative of the out-migrantcommunities, we developed a set of weights to reflect the relative contribution of U.S.households to the total binational sample. The weights, which are applied to each case, arethe inverse of the sampling fraction employed at each site (Sudman 1983). In the Mexicancommunities, sampling fractions were the number of sample households divided by thenumber of eligible households on the sampling frame. In the United States, we estimatedsampling fractions by dividing the number of sample households by the estimated size of theout-migrant community.


We derived the latter estimate using data on the current location of children of thehousehold head who were no longer household members. Following Massey and Parrado(1994), we determined the number of nonmember children who were living in the UnitedStates and Mexico at the time of the survey, and formed the ratio between them to indicatethe relative size of the U.S. community. We then applied this ratio to the Mexican samplingframe to estimate the total size of the out-migrant community.

In general, the Mexican community samples represent conditions in the core sendingregion at the time of the survey, while the U.S. surveys depict conditions in thecorresponding out-migrant communities at roughly the same time. When pooled andweighted, the surveys offer a comprehensive portrait of 22 binational communities that havebeen created through recurrent U.S. migration and settlement. In choosing our study sites,we sought to include a range of community population sizes, ethnic compositions, andeconomic bases. Although our sample technically does not represent the states of westernMexico, nonetheless it reflects a broad cross-section of households and communities in theregion.

Respondents were interviewed with ethnosurvey methods (Massey 1987). From eachhousehold head we gathered a complete life history that included a detailed inventory ofborder crossings. For each trip to the United States, undocumented migrants told us the yearof the crossing and the number of times they were apprehended by the INS while trying toenter. The number of apprehensions per trip is the basic datum analyzed in this study.

ESTIMATING THE ANNUAL PROBABILITYOF APPREHENSION

We selected all trips made by undocumented household heads between 1965 and thesurvey date, and examined the number of times each person had been apprehended beforefinally gaining entry to the United States. We begin in 1965 because that year represents awatershed in the history of immigration. In 1965 Congress passed a major revision of U.S.immigration law which is generally credited with shifting the composition of immigrationaway from Europe and toward Latin America (Reimers 1985). In addition, Congress endeda temporary worker program which had arranged, over the preceding 22 years, for theimportation of a total of some 4.6 million Mexican guest workers (Calavita 1992).

A total of 1,229 undocumented migrants provided data on 3,207 trips to the UnitedStates. Nearly all of the respondents were men. Our sample of household heads containedonly 39 females with U.S. migrant experience, accounting for just 2.3% of all trips. Thedistribution of trips by number of apprehensions was highly skewed. Most migrants reportedno apprehensions at all: on 71 % of the trips the number was zero; on 18%, one; on 6%, two;on 3%, three; and on I % four.

These figures do not suggest that apprehension stops the aspiring undocumentedmigrants: 98% of all respondents entered the United States after five or fewer attempts, andmore than two-thirds succeeded on the first try. An unlucky few had more trouble: about 2%reported five or more apprehensions, and one hapless soul reported 20 separate arrestsbefore finally gaining entry. The figure of 71% with no apprehensions is very close to thefigure of 68% reported by men legalized under the Immigration Reform and Control Act(U.S. Immigration and Naturalization Service 1992), and adds credibility to our estimates.

The number of apprehensions per trip may be conceptualized as a discrete randomvariable determined by an underlying Poisson probability process (Kenkel 1989). Therefore,to calculate annual probabilities of arrest, we used Poisson regression to express the number


of apprehensions per trip as a function of dummy variables representing single years from1966 through 1992; 1965 served as the reference category (Computing Resource Center1992).

In estimating the equation, we employed case weights and set the exposure parameterequal to the number of attempted crossings (i.e., the number of reported apprehensions plus1). The Poisson probabilities we calculated thus give the likelihood of apprehension perattempted crossing as reported by respondents in our binational sample. AlthoughEspenshade (1990) was able to compute this probability on a monthly basis, our data allowonly annual computations.

Table 2 presents the results of the Poisson regression. Aside from the dummy variablesfor year, the model includes no other predictors. Even so, we recognize that the odds ofapprehension are likely to be affected by personal and household circumstances, and bymacro-level factors such as the size of the migrant cohort and the number of Border Patrolofficers deployed (see Espenshade and Acevedo 1993). Our purpose here is not to explainwhy a particular probability occurred in a given year, but to use a reliable statistical methodto determine the annual probability of apprehension. We have prepared a separate analysisto determine how individual, household, community, and macro-level factors influence theprobability of apprehension (see Singer, Donato, and Durand, 1994).

The three left-hand columns of Table 2 contain estimated Poisson regressioncoefficients, their standard errors, and associated p-values. Most of the coefficients differsignificantly from 0, thus suggesting considerable year-to-year variation in the annualprobability of apprehension. Notable peaks occur in 1973, 1976, 1978, and 1980; troughsare observed in 1969, 1985, 1988, and 1991. Although the coefficient for 1992 is stronglynegative, the number of trips taken that year is quite small, and the coefficient is unreliablyestimated and statistically insignificant.

In general, the numerical values of the coefficients tend to decrease over time,indicating a secular decline in the probability of apprehension. This trend is most evident inthe Poisson probabilities shown in the fourth column of Table 2. Because these figures areestimated from a sample rather than from a complete enumeration of all migrants in thesending communities, some of the year-to-year variation reflects sampling error in additionto other measurement errors. To generate more consistent and more stable indicators of thegeneral trend, we computed three-year moving averages of the Poisson probabilities, whichare shown in the last column of the table.

The smoothed probabilities reveal the general trend toward lower likelihoods ofapprehension after 1982. Until then, the probability of apprehension per attempt was fairlystable, generally ranging between .36 and .42. From 1965 to 1982, the smoothedprobabilities of apprehension fell outside this range only twice: in 1965 (when the smoothedlikelihood was .255) and 1970 (when it dropped to .306). After 1982, however, smoothedapprehension probabilities fell steadily and never again reached even the lower limit of the1965-1982 range.

The decline is captured clearly in averages computed for successive five-year intervals.During the period 1965-1969, the average apprehension probability was .35; during1970-1974 it was .38; during 1975-1979 it was .41. By the time we reach 1980-1984, themean probability of apprehension has fallen to .34; by 1985-1989 it is .27. Althoughestimates for the early 1990s must be interpreted cautiously because of small numbers (mostof the community samples were taken before 1992), the likelihood of apprehension appearsto decline even further after 1989, reaching an average of just .09 during 1990-1992.

We attempted to validate these probability estimates by comparing them with theresults of other empirical studies based on defensible analytic methods. Espenshade (1990),for example, computed and estimated an average probability of apprehension of .32 for theperiod 1977-1988. When we computed the mean Poisson probability for the same period,


Table 2. Poisson Regression of the Number of Reported Apprehensions on the Year ofthe Trip: Undocumented Mexican Migrants from 22 Communities, 1965 - 1992

EstimatedPoisson Regression Probability per Attempt

Year of Standard Poisson SmoothedU.S. Trip Coefficient Error P- Value Probability Series

1965 .272 .2551966 -0.135 0.138 0.327 .237 .3681967 0.785** 0.089 0.000 .595 04351968 0.558** 0.091 0.000 0474 04171969 -0.398** 0.112 0.000 .182 .3341970 0.240** 0.090 0.008 .345 .3061971 0.363** 0.088 0.000 .390 .3581972 0.222* 0.090 0.014 .339 .3981973 0.538** 0.084 0.000 0465 .3881974 0.279** 0.089 0.001 .359 04171975 00451** 0.084 0.000 0426 04121976 0.508** 0.084 0.000 0451 04121977 0.282** 0.085 0.001 .360 04231978 0.520** 0.083 0.000 0457 .3921979 0.276** 0.084 0.001 .358 .4151980 00460** 0.083 0.000 0430 .3921981 0.355** 0.084 0.000 .387 .3661982 0.039 0.089 0.659 .282 .3291983 0.158 0.086 0.070 .318 .2911984 0.006 0.086 0.943 .273 .2681985 -0.245** 0.089 0.006 .213 .2811986 0.274** 0.085 0.001 .357 .3031987 0.219* 0.088 0.013 .338 .2671988 -0.937** 0.109 0.000 .105 .2671989 0.279** 0.092 0.003 .359 .2311990 -0.167 0.099 0.092 .230 .2101991 - 1.887** 0.276 0.000 .041 .0901992 -11.722 35.083 0.738 .000 .020Constant - 1.304** 0.080 0.000Log Likelihood 27522**Chi-Square 26482**Number of Trips 3,207

* p <.05; ** p<.Ol.

we obtained exactly the same figure. Likewise, Crane et al. (1990) computed a meanprobability of .30 for the period 1970-1988. Our average for the same span was slightlyhigher at .35. Finally, Kossoudji (1992) derived a median apprehension probability of .33for the period 1974 through 1978; our figure was higher at AI.

In general, our estimates replicate fairly closely the prior estimates of the apprehensionprobability. In one case we obtain exactly the same result, and in two other cases thedeviations are .05 and .08. The average deviation from prior work is only .04, representinga mean error rate of about 12%. On the basis of this analysis, it seems safe to conclude that


the probability of apprehension for undocumented Mexican migrants attempting to cross thesouthern border of the United States varies roughly from .20 to .40 and averages around.33. As other studies have found, the odds of apprehension are relatively low and do notseem to offer much of a deterrent to would-be migrants (Espenshade 1994).

ESTIMATING GROSS AND NET UNDOCUMENTEDMIGRATION FROM MEXICO

Given valid and reliable estimates of the annual probability of apprehension, we canapply Eqs. (2) and (3) to derive estimates of gross and net undocumented migration fromMexico for the period 1965 through 1989. Table 3 reports the results of this estimation.Columns 1-4 summarize the computation of annual gross undocumented migration. Thefirst column contains the smoothed annual probabilities, p, from Table 2; Column 2computes the adjustment factor (l-p)/p; Column 3 shows the number of Mexicans who wereapprehended while trying to cross the border (from INS statistics); and Column 4 shows theproduct of Columns 2 and 3, which represents our estimate of the gross inflow ofundocumented migrants into the United States by year.

The figures in Column 4 reveal the tremendous growth in undocumented Mexicanmigration that occurred after 1965. Beginning in that year, the number of Mexicans enteringthe United States illegally expanded year by year until the late 1970s. From only 87,000 in1965, the number grew by an average annual rate of 20% to reach 1.47 million in 1978.Then it stabilized until 1981, fluctuating between 1.2 and 1.5 million undocumented entriesper year. These years of comparative stability coincide with Mexico's oil boom, whenwages, employment rates, and exchange rates were unusually favorable on the Mexican side(see Gregory 1986).

In 1982, however, the oil bubble burst, ushering in Mexico's worst economic crisissince 1910 (Sheahan 1991). In that year, illegal entries once again began a sustained risethat culminated in 1986, when Congress passed the Immigration Reform and Control Act(lRCA) in an effort to curb the flow. From 1.49 million undocumented entries in 1981, theflow grew each year and reached 3.82 million in 1986, more than doubling in just fiveyears. The flow then fell to 2.59 million in 1988 but rose again to 2.85 million in 1989.Although illegal entries clearly declined during the late 1980s, the change does notnecessarily indicate a new deterrent resulting from the IRCA. Many undocumented migrantsstopped crossing the border because they decided to stay in the United States to apply forlegalization through the IRCA, thereby reducing the number of apprehensions (Bean et al.1990).

During the 25-year period from 1965 to 1990, we estimate 36.5 million undocumentedentries from Mexico. This inflow, however, does not mean that 36.5 million illegalresidents were added to the U.S. population because it ignores a substantial return flow,adjustments in legal status that occurred after entry, and deaths to illegal immigrants in theUnited States. By any standard, however, the scale of movement between Mexico and theUnited States is immense.

In Column 5 of the table, we compute the ratio of entries minus departures over entries,the adjustment factor used to convert gross into net entries (see Eq. (3». As before, tocontrol for fluctuations attributable to sampling and other errors, we smoothed theadjustment factors using three-year moving averages. Multiplying the adjustment factors inColumn 5 by the gross flows reported in Column 4 yields the estimates of net undocumentedmigration shown in Column 6.

The adjustment factors in Column 5 indicate the remarkable circularity of Mexican


Table 3. Estimated Probabilities of Apprehension, Gross Undocumented Migration, andNet Undocumented Migration of Mexican Migrants to the United States,1965-1989

(1) (2) (3) (4) (5) (6)Probability Apprehensions Estimated Ratio of Estimated

of Recorded Gross Entries minus NetApprehension by INS· Undocumented Departures Undocumented

Year p (1- p)/p (000) In - Migration over Entries In - Migration

1965 .255 2.922 29.7 86.8 .229 19.91966 .368 1.717 57.9 99.4 .334 33.21967 .435 1.299 77.6 100.8 .398 40.11968 .417 1.398 117.2 163.8 .459 75.21969 .334 1.994 161.7 322.4 .487 157.01970 .306 2.268 239.9 544.1 .298 162.11971 .358 1.793 312.9 561.0 .346 194.11972 .398 1.513 391.9 592.9 .336 199.21973 .388 1.577 542.2 855.0 .407 348.01974 .417 1.398 681.1 952.2 .400 380.91975 .412 1.427 654.8 934.4 .278 259.81976 .412 1.427 757.4 1,080.8 .290 313.41977 .423 1.364 920.9 1,256.1 .263 330.41978 .392 1.551 948.9 1,471.7 .288 423.81979 .415 1.410 977.7 1,378.6 .238 328.11980 .392 1.551 802.1 1,244.1 - .015 -18.71981 .366 1.732 859.7 1,489.0 - .023 -34.21982 .329 2.040 870.8 1,776.4 -.094 -167.01983 .291 2.436 1,157.9 2,820.6 .170 479.51984 .268 2.731 1,159.1 3,165.5 .199 629.91985 .281 2.559 1,257.1 3,216.9 .244 784.91986 .303 2.300 1,662.0 3,822.6 - .089 - 340.21987 .267 2.745 1,133.1 3,110.4 .015 46.71988 .267 2.745 943.1 2,588.8 - .057 -147.61989 .231 3.329 856.6 2,851.6 .229 653.0Total .349 17,573.3 36,485.9 .141 5,151.5

a The total number of Mexicans arrested for entry without inspection in the year indicated(Statistical Yearbook of the Immigration and Naturalization Service, various years).

migration. In 25 years, the adjustment factor never exceeded .46; that is, nearly half of allentries were offset by departures in the year of strongest net entry. Usually thecountervailing effect of departures was much greater: the average adjustment factor of .141suggests that overall, 86% of Mexican entries were offset by departures. The adjustmentfactor tends to favor entries most strongly during the late 1960s and early 1970s, when itvaried above .30, but thereafter it fell and even became negative at several points during the1980s. The factor reached its nadir during the oil boom years of 1980-1982 and thehyperinflation years of 1986-1988. During the latter period, the real exchange rate peaked,so that people with dollars could return to Mexico and buy up goods denominated in pesosat extremely cheap prices (see Sheahan 1991).

Adjusting for return migration yields estimates of net undocumented migration that aresubstantially below the figures for gross entries. In general, net undocumented migration


expanded steadily from 1965 through 1978 and then fell steeply to bottom out in 1982; inthat year the flow was actually negative. During the years of Mexico's economic crisis,however, the flow fluctuated sharply, reflecting the instability of exchange rates andeconomic conditions in the country from 1982 to 1989.

Overall, we estimate that the U.S. population received a net increment of 5.2 millionMexicans after 1965 as a result of undocumented migration, constituting just 14% of thetotal number of undocumented entries. Once again, however, this figure does not mean thatthe number of undocumented Mexicans living in the United States was 5.2 million in 1990.Our estimate makes no adjustment for the death of undocumented migrants after entry, orfor changes in legal status made through the IRCA amnesty or the normal provisions of U.S.immigration law. Such adjustments would reduce the estimate of the number ofundocumented migrants in 1990.

CONCLUSIONS

Using a new source of data gathered among migrants from 22 Mexican communities,we computed empirical estimates of the annual probability of apprehension forundocumented migrants crossing the border from 1965 through 1989. Our estimates confirmthose obtained by other researchers using different methods and data. As far as we candiscern, the probability of apprehension over the past 25 years has varied from .20 to .40,and has averaged around 33%. The odds of being caught while trying to cross the borderillegally thus appear to be about 1 in 3, although our analysis suggests that the odds ofevading arrest may have improved in recent years.

We applied our estimates of the annual probability of apprehension to INSapprehension statistics, using a formula derived by Espenshade (1990) to compute theannual number of undocumented entries from Mexico. We found that the gross inflow ofundocumented Mexican migrants grew by an average of 20% per year from 1965 to 1978,when it reached nearly 1.5 million. It then leveled off until the onset of Mexico's economiccrisis initiated another period of rapid expansion, which peaked at 3.8 million in 1986. Theannual number of entries then fell into the 2.5-3 million range from 1986 through 1989.During the 25 years leading up to 1990, we calculate a total of 36.5 million entries byundocumented Mexicans. This estimate is broadly consistent with recent national surveysmade in Mexico, which reveal that one-third of all Mexicans have been to the United Statesat some point in their lives (Camp 1993).

Our analysis also reveals a strong return flow that substantially offsets the huge inflowof undocumented Mexican migrants. Earlier studies noted this circularity, but ours is thefirst to document its effect in substantially counterbalancing the high rates of illegal entry.Over the 25-year period under study, 86% of all entries were offset by departures, yieldinga net inflow of only 5.2 million. The relative surplus of entries over departures was greatestduring the 1960s and early 1970s; net undocumented migration grew steadily through 1974before leveling off during the later 1970s. After 1980 we observe several periods of netoutflow, and net migration fluctuated quite sharply during the Mexican economic crisis of1982-1989.

Our data suggest that by the late 1980s the probability of apprehension was driftingdownward from its historical average of around .33, that 3.1 million undocumentedMexicans were entering the United States each year, and that 2.9 million were departingannually. Taken together, these facts suggest an increasingly porous border characterized bymassive circulation and limited deterrence through apprehension. The odds of being caughton any given attempt appear to be decreasing, and nearly everyone succeeds in entering


after a few attempts. Under these circumstances, most of the aspiring migrants simply makerepeated attempts until they are successful.

Our conclusions are sustained by recent experiences along the U.S.-Mexico border. Inan effort to meet growing demands for action, the U.S. Immigration and NaturalizationService in 1993 launched "Operation Hold the Line" in El Paso. This program greatlyincreased the personnel, resources, and effort that the local office of the Border Patroldevoted to enforcement.

The program appears to have succeeded in deterring Mexican teens from entering forrecreational purposes and in halting sidewalk vendors from entering for commercialpurposes, but it has had little effect on long-distance migrants or daily commuters enteringfor work (Bean 1994). Most of these people now simply go around the El Paso sector andeuter through Arizona: in the Tucson district, for example, arrests of Mexican migrantsincreased by 40% between 1993 and 1994 (Sanchez 1994). Thus, for millions of Mexicans,the border apparently has become a fading line between two countries whose societies andeconomies are increasingly integrated.

REFERENCES

Bean, F.D. 1994. Testimony before Hearings by the Commission on Immigration Reform, EI Paso,March 18-19.

Bean, F.D., T.J. Espenshade, M.J. White, and R.F. Dymowksi. 1990. "Post-IRCA Changes in theVolume and Composition of Undocumented Migration to the United States: An AssessmentBased on Apprehensions Data." Pp. Ill-58 in Undocumented Migration to the United States:IRCA and the Experience of the I980s, edited by F.D. Bean, B. Edmonston, and J.S. Passel.Washington, DC: Urban Institute.

Calavita, K. 1992. Inside the State: The Bracero Program, Immigration, and the I.N.S. New York:Routledge.

Camp, R.A. 1993. Politics in Mexico. New York: Oxford University Press.Computing Resource Center. 1992. Stata Reference Manual, Vol. 3. Santa Monica: Computing

Resource Center.Crane, K., B.J. Asch, J.Z. Heilbrunn, and D.C. Cullinane. 1990. The Effect of Employer Sanctions

on the Flow of Undocumented Immigrants to the United States. Santa Monica: RAND.Donato, K.M., J. Durand, and D.S. Massey. 1992. "Stemming the Tide? Assessing the Deterrent

Effects of the Immigration Reform and Control Act." Demography 29:139-58.Durand, J., and D.S. Massey. 1992. "Mexican Migration to the United States: A Critical Review."

Latin American Research Review 27:3-42.Espenshade, T.J. 1990. "Undocumented Migration to the United States: Evidence from a Repeated

Trials Model." pp. 159-81 in Undocumented Migration to the United States: IRCA and theExperience of the 1980s, edited by F.D. Bean, B. Edmonston, and J.S. Passel. Washington, DC:Urban Institute.

___. 1994. "Does the Threat of Apprehension Deter Undocumented U.S. Immigration?"Population and Development Review 20:871-92.

Espenshade, T.J., and D. Acevedo. 1995. "Migrant Cohort Size, Enforcement Effort, and theApprehension of Undocumented Aliens." Population Research and Policy Review, forthcoming.

Goodman, L. 1961. "Snowball Sampling." Annals of Mathematical Statistics 32:117-51.Gregory, P. 1986. The Myth of Market Failure: Employment and the Labor Market in Mexico.

Baltimore: Johns Hopkins University Press.Jones, R C. 1988. "Micro Source Regions of Mexican Undocumented Migration." National

Geographic Research 4:11-22.Kenkel, J.L. 1989. Introductory Statistics for Management and Economics. Boston: PWS-Kent.Kossoudji, S.A. 1992. "Playing Cat and Mouse at the U.S.-Mexican Border." Demography

29:159-80.


Massey, D.S. 1987. "The Ethnosurvey in Theory and Practice." International Migration Review21:1498-1522.

Massey, D.S., L.P. Goldring, and J. Durand. "Continuities in Transnational Migration: An Analysisof 19 Mexican Communities." American Journal of Sociology 99: 1492-1533.

Massey, D.S., and E. Parrado. 1994. "Migradollars: The Remittances and Savings of MexicanMigrants to the United States." Population Research and Policy Review 13:3-30.

Reimers, D.M. 1985. Still the Golden Door: The Third World Comes to America. New York:Columbia University Press.

Sanchez, R. 1994. "Arizona Border Swamped as Illegals Seek Easy Entry." Phoenix Gazette, March18, p. 1.

Sheahan, J. 1991. Conflict and Change in Mexican Economic Strategy: Implications for Mexico andLatin America. La Jolla: Center for U.S.-Mexican Studies, University of California, San Diego.

Singer, A., K.M. Donato, and J. Durand. 1994. "The Social Process of Border Crossing:Undocumented Mexican Migrants to the United States." Presented at the annual meetings of thePopulation Association of America, Miami.

Sudman, S. 1983. "Applied Sampling." Pp. 145-94 in Handbook of Survey Research, edited by P.H.Rossi, J.D. Wright, and A.B. Anderson. Orlando: Academic Press.

U.S. Immigration and Naturalization Service. 1992. Immigration Reform and Control Act: Report onthe Legalized Alien Population. Washington, DC: U.S. Government Printing Office.

new estimates of undocumented mexican migration and the probability of apprehension

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