Illegal Immigration: INS Overstay Estimation Methods Need Improvement
(Letter Report, 09/26/95, GAO/PEMD-95-20).

Reliable and valid estimates of the number of overstays--persons who
entered the United States legally as visitors but did not leave under
the terms of their admissions--are important to public policy-making.
Higher number of overstays might suggest, for example, the need for
stricter policies or laws for issuing temporary U.S. visas to citizens
of those countries whose travelers tend to overstay their visas in
significant numbers. Overstay data are also needed to monitor travel
from countries whose citizens are not required to obtain a U.S. tourist
visa. This report examines the basis for the Immigration and
Naturalization Service (INS) estimates of overstays and suggests ways in
which estimates of immigrant overstays can be improved by INS.

--------------------------- Indexing Terms -----------------------------

 REPORTNUM:  PEMD-95-20
     TITLE:  Illegal Immigration: INS Overstay Estimation Methods Need 
             Improvement
      DATE:  09/26/95
   SUBJECT:  Illegal aliens
             Resident aliens
             Travel
             Immigration and naturalization law
             Airline industry
             Immigration or emigration
             Statistical data
             Statistical methods
             Management information systems
IDENTIFIER:  INS Nonimmigrant Information System
             INS Visa Waiver Pilot Program
             Bahamas
             France
             Germany
             Haiti
             India
             Mexico
             Philippines
             Poland
             Soviet Union
             
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Cover
================================================================ COVER


Report to the Chairman, Subcommittee on Immigration, Committee on the
Judiciary, U.S.  Senate

September 1995

ILLEGAL IMMIGRATION - INS OVERSTAY
ESTIMATION METHODS NEED
IMPROVEMENT

GAO/PEMD-95-20

INS Overstay Estimation Methods Need Improvement

(973802)


Abbreviations
=============================================================== ABBREV

  CD - Counted departures
  EXD - Expected departures
  INS - Immigration and Naturalization Service
  NIIS - Nonimmigrant Information System
  OV - Overstays
  R(OV) - Rate of overstay
  TD - True departures
  UCD - Uncounted departures
  URDF - Unrecorded departure forms

Letter
=============================================================== LETTER


B-261245

September 26, 1995

The Honorable Alan K.  Simpson
Chairman, Subcommittee on Immigration
Committee on the Judiciary
United States Senate

Dear Mr.  Chairman: 

This letter is in response to your April 18, 1995, request that we
examine the basis for the Immigration and Naturalization Service
(INS) estimates of overstays--that is, persons who entered the United
States legally as visitors but did not leave under the terms of their
admission.  INS estimates that about half of the illegal resident
aliens in the United States during recent years have been overstays. 
The other half are principally persons who crossed U.S.  borders
illegally. 

Reliable and valid estimates of the number of overstays are important
to public policy-making.  Higher numbers of overstays might suggest,
for example, the need for stricter policies or laws for issuing
temporary U.S.  visas to citizens of those countries whose travelers
tend to overstay their visas in significant numbers.  Higher numbers
of illegal border crossers might suggest a greater need for actions
such as further improving border security.  Overstay data are also
needed to monitor travel from countries whose citizens are not
required to obtain a U.S.  tourist visa.\1


--------------------
\1 Twenty-three countries (mostly advanced industrial countries) are
currently included in the Visa Waiver Pilot Program, extended through
Sept.  30, 1996, by Public Law 103-416, sec.  210, Oct.  25, 1994. 
If the overstay rate INS estimates for a country in the pilot program
is above a specified threshold, that country must be removed from the
program.  The full list of current visa-waiver pilot countries is
given in appendix I, footnote 4, p.  17. 


   BACKGROUND
------------------------------------------------------------ Letter :1

The task of estimating overstays presents a difficult challenge. 
Although INS has a data system for tracking the dates when individual
foreign visitors arrive in and depart from the United States, the
agency cannot assume that all persons whom the system does not record
as having left have, in fact, overstayed their lawful periods of
entry. 

Most foreign visitors tracked by the INS data system travel to the
United States by air.\2 The INS data system works as follows: 
Airline personnel distribute arrival/departure forms (I-94s) to
foreign visitors.\3 An INS inspector collects the arrival portion of
the form as each visitor enters the United States; at that time, the
inspector staples the departure form in the visitor's passport.  The
airlines are responsible for collecting the departure forms when
visitors leave and for sending those forms to INS.  But for some
visitors who may have actually left the United States, INS apparently
has no record of the departures.  It is thus not clear, in any
particular instance, whether an "unrecorded departure form"
represents a person who overstayed or whose actual departure went
uncounted. 


--------------------
\2 INS' Nonimmigrant Information System (NIIS), which tracks
nonimmigrant visitors to the United States, does not include (1)
certain categories of Canadian visitors or (2) Mexican visitors whose
travel is limited to an area within 25 miles of the U.S.-Mexican
border for periods of no more than 72 hours.  The system also does
not include foreign students (or their dependents) admitted to study
at U.S.  colleges, universities, or vocational schools. 

\3 The information requested on the arrival form includes airline of
entry, sex, date of birth, and certain other data.  (The form is
reproduced as figure I.1 in appendix I.)


   OBJECTIVES, SCOPE, AND
   METHODOLOGY
------------------------------------------------------------ Letter :2

Our objectives were to examine the basis of INS overstay estimates
and, as appropriate, to suggest improved estimation procedures.  In
reviewing the agency's methodology, we examined published documents
that describe INS procedures and interviewed staff about their
methods of overstay estimation, the kinds of data that are available,
and the potential for devising improved overstay estimates.\4 We
focused primarily on tourist air arrivals since they represent the
majority of the foreign visitors in the INS data system.\5 We
developed new estimation procedures and applied them to tourist
visitors arriving by air in the United States from nine countries
from October 1990 to March 1991.\6 We also talked with officials from
the Department of State about their use of INS estimates and asked a
number of experts to review a draft of this report.\7

We conducted our review in accordance with generally accepted
government auditing standards. 


--------------------
\4 Our review did not include an assessment of the validity of the
criteria INS used to select the "index" countries (which, as
explained in a subsequent section, are used to estimate uncounted
departures). 

\5 Other than Mexican and Canadian visitors (who often enter this
country by land), most foreign visitors arrive by air. 

\6 INS provided us with these data from its Nonimmigrant Information
System. 

\7 The expert reviewers are listed in appendix III. 


   RESULTS IN BRIEF
------------------------------------------------------------ Letter :3

Despite difficulties in obtaining accurate departure data, INS
devised a creative approach for estimating overstays through
estimating the number of uncounted departures (that is, "system
error").  Specifically, INS determined that system error could be
estimated by using data from countries for which it seems safe to
assume there are few or no overstays (that is, "index countries"). 
INS applied its index countries' strategy using a "global" approach
that requires the assumption that a single rate of system error
applies to all countries worldwide.\8 We believe that this assumption
is questionable and that improved approaches have the potential to
reduce the uncertainty of current INS estimates. 

We devised an alternative method for estimating overstays among
foreign visitors who arrive by air.  Our method is based on INS'
index country strategy but uses more detailed INS data and avoids the
global assumption.  Our method also corrects an error in INS'
computation formula\9 and uses appropriately weighted data.  (INS did
not weight the data.) When we applied our method to sample INS data
for nine nonindex or sending countries, we found overstay estimates
that are, on average, lower than corresponding INS estimates.\10
Specifically, our estimates are between 16 percent and 47 percent
lower than INS'.  (See table 1 on p.  8.  While these are not
worldwide estimates, the nine sending countries do account for over
one-third of all overstays in the tourist air arrival class.)

INS' global approach provided a good starting point for estimating
overstays.  Our approach is different mainly in that it makes more
limited assumptions.  We believe this may reduce the uncertainty of
the estimates.  In response to early presentations of our work, INS
and other experts suggested additional strategies for reducing the
uncertainty of overstay estimates.  (See appendix I.) We believe that
INS should develop improved procedures for estimating overstays,
using methods such as those discussed in this report. 


--------------------
\8 If this assumption does not hold true, the resulting estimates of
overstays would be inaccurate--at least for certain countries and
possibly worldwide. 

\9 For tourists arriving by air, the resulting error in INS' estimate
is on the order of 7 to 10 percent. 

\10 These nine sending countries are the Bahamas, France, Germany,
Haiti, India, Mexico, Philippines, Poland, and the former Soviet
Union. 


   GAO'S ANALYSIS
------------------------------------------------------------ Letter :4

INS considers the pool of unrecorded departure forms to represent two
groups of persons--true overstays and uncounted departures.\11 For
true overstays, no departure forms were ever turned in because these
visitors never left the United States.  For uncounted departures,
there was a paperwork error of some sort; that is, these visitors did
leave but their departures were not counted by INS (either because
the airline did not collect their departure forms or for some other
reason).  INS has termed the unrecorded departure forms in this
latter group "system error." Earlier we noted that one could not
simply assume that all unrecorded departure forms represent
overstays.  Here we see that some unrecorded departure forms
represent system error.  In short, true overstays equal unrecorded
departure forms minus the number attributable to system error. 

In order to estimate true overstays, INS thus needs to estimate
system error.  INS does this using 11 "index countries" that it
believes have so few true overstays that all unrecorded departure
forms can be considered uncounted departures (system error).\12 If
INS finds, for example, that 10 percent of airline travelers arriving
from these index countries were not counted as departures, the agency
then assumes that the percentage of uncounted airline departures is
about 10 percent in all countries.\13

That is, INS uses one estimate of the percentage of uncounted
departures for all countries of the world. 

INS' specific method of estimating overstays from each country is to
subtract an estimate of uncounted departures from the total number of
unrecorded departure forms for each country, based on a global
estimate of the proportion of departure forms that are missing
because of system error.  INS then totals the individual countries'
overstay estimates to produce an estimate of the number of true
overstays from all countries.\14

While this method is creative, it makes a sweeping assumption.  INS
itself had characterized its procedures as more likely to
overestimate than underestimate the number of overstays.  Officials
from the Department of State also questioned the accuracy of INS'
estimates of overstays for certain countries.\15

In a detailed review, we found that estimates based on INS' global
approach are necessarily marked by considerable uncertainty because
of the assumption that rates of system error are the same for index
countries and all other countries.  Although INS' procedures assume
it is safe to ignore the potential for differences in system error
between index countries and other countries, airline-specific data
for the index countries showed evidence to the contrary:  First, INS'
airline-specific data confirmed that citizens of different countries
tend to fly to the United States on different airlines.  Second, INS'
airline-specific data for index countries showed that there is
substantial variation in system error across airlines. 

We also found an algebraic error in INS' computation formula.  INS'
use of an incorrect formula resulted in an error on the order of 7 to
10 percent in INS' overstay estimates for air travelers.\16


--------------------
\11 In this report, we use the terms "true overstay" and "overstay"
interchangeably.  We use the term "unrecorded departure forms" where
INS has used the term "apparent overstays."

\12 The index countries are Australia, Belgium, Finland, Netherlands
Antilles, New Zealand, Norway, Saudi Arabia, Sweden, Singapore,
Suriname, and Switzerland.  INS dropped Kuwait, a country it had
originally included as an index country, because of increased
overstays resulting from the Gulf war.  With respect to the
assumption that the index countries have virtually no true overstays,
we note that all sizable countries, including index countries,
probably have at least some "technical overstays." (See footnote 10
in appendix I.)

\13 As explained in appendix I, INS adds an adjustment to this figure
when estimating uncounted departures for nonindex countries.  This
adjustment accounts for the fact that index countries may have
slightly lower rates of uncounted departures than other countries. 
(An upward adjustment seems justified because one criterion INS used
in selecting the index countries was low rates of unrecorded
departure forms.)

\14 INS uses the same procedure to separately estimate overstays who
arrived by air, land, and sea.  (See appendix I, pp.  42-43, for a
discussion of land overstays.)

\15 That is, they told us they believed certain estimates did not
seem plausible in view of the State Department's experience with or
knowledge about those countries. 

\16 The specific effect of the error in INS' computation formula--in
and of itself--is to underestimate overstays.  The specific size of
the difference in estimates owing to this error varies according to
the particular data in question.  See appendix I, pp.  28-30, for a
detailed explanation of the error. 


      GAO'S METHOD
---------------------------------------------------------- Letter :4.1

We devised a method that uses INS' airline-specific data for index
countries as the basis for estimating separate rates of system error
for each airline.  We explain this method in detail below, but the
main point is that it allows us to estimate system error separately
for each airline---rather than rely on the assumption that a single
rate of system error applies to all flights from all countries of the
world. 

Specifically, we began by estimating system error separately for each
airline that regularly flies between one or more index countries and
the United States.\17 For example, we used the rate of unrecorded
departure forms for index country passengers on United Airlines to
estimate system error for all United Airlines flights.\18

We repeated this procedure, estimating system error separately for
Delta Air Lines, Air Micronesia, and so forth, on the basis of index
countries' data for each airline. 

Then, we estimated overstays for nonindex countries--proceeding
separately, country by country and airline by airline.  For example,
we estimated overstays from the Philippines who flew to this country
on United Airlines using the specific rate of system error we had
estimated for United Airlines; then we estimated overstays from the
Philippines who flew in on Air Micronesia using the estimated rate of
system error for Air Micronesia, and so forth.  Essentially, we
assumed that system error on United Airlines flights between the
Philippines and the United States was about the same as for United
Airlines flights between index countries and the United States.  We
made the same assumption for Air Micronesia flights, and so forth. 

For some airlines, this approach was not possible because they do not
regularly fly between any index country and the United States.  For
these "nonqualifying" airlines, additional assumptions were
necessary.  In making assumptions, we wished to be as conservative as
possible.  We therefore calculated two sets of estimates using
alternative assumptions, as described below. 


--------------------
\17 This approach was suggested by ongoing analyses at INS in which
data on unrecorded departure forms were crosstabulated separately,
airline by airline.  It uses INS' index countries' strategy but
carries it further. 

\18 That is, INS selected the index countries because visitors from
these countries are apparently so unlikely to overstay that it may be
reasonable to assume that virtually none are true overstays. 
Assuming that virtually none of the United Airlines passengers from
the index countries overstayed, the rate of unrecorded departure
forms calculated for index countries' visitors who flew in on United
Airlines represents a rate of uncounted departures--or system error
for that airline.  Following the INS procedure described in footnote
13 (and in appendix I), we added one standard deviation to the rate
of uncounted departures calculated for index countries' passengers on
United Airlines.  Unlike INS, we always used weighted data. 


         ASSUMPTION 1 FOR
         NONQUALIFYING AIRLINES: 
         SAME OVERSTAY RATES
-------------------------------------------------------- Letter :4.1.1

We first assumed that passengers on nonqualifying airlines have the
same overstay rate as passengers from the same sending country who
arrived in the United States on qualifying airlines (for which the
separate calculations could be performed). 

The example of Mexico can illustrate how our method works when this
assumption is used.  Separate estimates of system error were
available for American Airlines, Delta Air Lines, United Airlines,
Air Micronesia, and other "qualifying" airlines (which fly between
index countries and the United States)--but not for airlines such as
Mexicana de Aviacion and Aeromexico.  We were thus able to calculate
separate overstay estimates for Mexican visitors who arrived on each
qualifying airline.  For Mexican visitors who arrived on
"nonqualifying" airlines that do not regularly fly between index
countries and the United States (such as Mexicana de Aviacion and
Aeromexico), we assumed that the overstay rate was the same as for
Mexican visitors arriving on qualifying airlines.  Using these
procedures, we obtained overstay estimates for nine nonindex, or
sending, countries. 


         ASSUMPTION 2 FOR
         NONQUALIFYING AIRLINES: 
         SAME RATES OF SYSTEM
         ERROR
-------------------------------------------------------- Letter :4.1.2

We also performed a second set of calculations for the nine
countries, using the alternative assumption that, for a particular
sending country, passengers on both types of airlines (qualifying and
nonqualifying) had the same rates of system error.\19

Again using the example of Mexico to illustrate, we calculated
separate overstay estimates for passengers on each qualifying airline
(American Airlines, United, Delta, Air Micronesia, and so
forth)--exactly as before.  We then assumed that for Mexicana de
Aviacion, Aero Mexico, and other nonqualifying airlines, the rate of
system error was the same as calculated for Mexicans who arrived on
qualifying airlines. 


--------------------
\19 Our second set of calculations is like INS' method in that it
makes assumptions about rates of uncounted departures (system error)
but not about overstay rates.  But it differs from INS' in that our
assumptions about rates of system error are more limited; that is,
unlike INS', our assumptions about system error do not involve
airlines that do not fly between the country in question and the
United States. 


      GAO'S ESTIMATES AND INS'
---------------------------------------------------------- Letter :4.2

We believe our method represents an improvement on two counts: 
First, the assumptions required are more limited than those required
by INS' global method because, to the extent possible, our method
relies on airline-by-airline estimates of system error.  Second, we
used a correct, mathematically derived formula, as well as
appropriately weighted data.\20

Table 1 presents our two sets of estimates, based on the alternative
assumptions for nonqualifying airlines, for nine sending
countries.\21



                                     Table 1
                     
                     GAO and INS Estimates of Overstays Among
                          Tourist Air Arrivals From Nine
                                   Countries\a



Continent
and                              Using         Using
sending         Expected    assumption    assumption     Incorrect     Corrected
country     departures\b           1\c           2\d     formula\e     formula\f
----------  ------------  ------------  ------------  ------------  ------------
North
 America
Bahamas          112,717           928         3,866         6,889         7,457
                                (0.8%)        (3.4%)        (6.1%)        (6.6%)
Haiti             20,382         1,904         3,238         3,208         3,461
                                (9.3%)       (15.9%)       (15.7%)       (17.0%)
Mexico           399,355         7,098        15,646        18,697        20,270
                                (1.8%)        (3.9%)        (4.7%)        (5.1%)
Europe
France           220,815         2,152         1,786         3,921         4,300
                                (1.0%)        (0.8%)        (1.8%)        (1.9%)
Germany          462,508         1,542         1,257             0             0
                                (0.3%)        (0.3%)           (0)           (0)
Poland            17,042         3,790         6,038         5,919         6,378
                               (22.2%)       (35.4%)       (34.7%)       (37.4%)
Soviet            22,220         2,308         1,926         2,181         2,356
 Union                         (10.4%)        (8.7%)        (9.8%)       (10.6%)
Asia
India             21,878         1,683         1,753         2,103         2,272
                                (7.7%)        (8.0%)        (9.8%)       (10.4%)
Philippine        29,905         3,337         3,755         3,946         4,258
 s                             (11.2%)       (12.6%)       (13.2%)       (14.2%)
================================================================================
Total nine     1,306,822        24,742        39,265        46,864        50,752
 countries                      (1.9%)        (3.0%)        (3.6%)        (3.9%)
================================================================================
Total          5,654,346            \g            \g       126,167            \g
 worldwide                                                  (2.2%)
--------------------------------------------------------------------------------
\a These nine countries represent 37 percent of the overstays that
INS estimated for tourist air arrivals.  Tourist air arrivals account
for 76 percent of all the overstays INS estimates.  The sample data
cover the period October 1990 to March 1991 and are from NIIS, which
does not include (1) certain categories of Canadian visitors or (2)
Mexicans with border-crossing cards that allow them to travel within
25 miles of the U.S.-Mexican border for periods of 72 hours or less. 
This table also excludes travelers who are not tourists--for example,
visitors for business purposes and temporary workers--and land and
sea arrivals.  However, the majority of foreign visitors captured by
the NIIS data are tourists who arrive by air.  All estimates in this
table were computed using estimates of system error based on the
following index countries:  Australia, Belgium, Finland, Netherlands
Antilles, New Zealand, Norway, Singapore, Suriname, Sweden, and
Switzerland. 

\b The percentage of expected departures on qualifying airlines were: 
Bahamas, 25.8; Haiti, 66; Mexico, 50.9; France, 83; Germany, 81.5;
Poland, 23.1; Soviet Union, 15.8; India, 68.7; and the Philippines,
53.9. 

\c Assumption 1 is that visitors flying to the United States on
nonqualifying airlines are characterized by the same overstay rate as
visitors from the same country flying here on qualifying airlines. 

\d Assumption 2 is that visitors flying to the United States on
nonqualifying airlines are characterized by the same rate of system
error as visitors from the same country flying here on qualifying
airlines. 

\e INS' calculations.  In preparing these estimates, INS used its
usual procedures and did not correct the computational error in its
formula. 

\f Our calculations, based on INS' global estimate of system error
and the correct formula, which is presented in appendix I.  Results
should be considered approximate because the system error (as
calculated by INS) was rounded to the nearest tenth of one percent. 

\g GAO did not calculate worldwide overstay estimates.

Table 1 also presents estimates of overstays based on INS' global
method; one column presents estimates calculated by INS using the
incorrect formula, and the other column presents estimates that we
calculated using INS' general global method but correcting the error
in INS' formula.\22

While results vary for individual countries, overstay estimates are,
on average, lower when using the more detailed airline-by- airline
method than when using the global method.\23 The contrast between
results using the global method and corresponding results using the
airline-by-airline method is greatest when the global method is
applied using the correct computation formula. 


--------------------
\20 In INS' calculation of system error, a large index country and a
small index country are given equal weight.  All our calculations are
weighted to represent the relevant number of visitors from each
country.  For example, in estimating system error for a particular
airline, data for index countries' passengers on that airline are
appropriately weighted to reflect the number of passengers from each
index country who flew here on that airline. 

\21 Of course, comparisons of our estimates to INS' for the nine
sending countries are not necessarily indicative of results that
would be obtained if estimates were calculated for all countries
worldwide. 

\22 Neither of the two sets of estimates based on INS' global method
was calculated using weighted data. 

\23 A key reason is that the airline-by-airline approach recognizes
that visitors from Mexico, the Philippines, and many other nations
are much more likely to fly to the United States on American carriers
than to use index countries' airlines such as Air New Zealand.  The
American carriers have relatively high rates of uncounted
departures--that is, relatively high rates of "system error." (See
table I.2 in appendix I.) The relatively high rates of system error
translate to lower estimates of overstays, since the number of
unrecorded departure forms is divided into system error (uncounted
departures) and overstays. 


      GAO'S ALTERNATIVE
      ASSUMPTIONS
---------------------------------------------------------- Letter :4.3

The airline-by-airline overstay estimates shown in table 1 are, on
average, lowest when passengers on nonqualifying airlines are assumed
to have the same overstay rates as passengers from the same country
who arrived on qualifying airlines.\24 Although the nine countries'
overstay estimates based on assumption 1 (totaling about 25,000) are
dramatically lower than INS', these might be the better of the two
sets of airline-by-airline estimates.\25 However, taken together, our
two sets of estimates for overstays from the nine sending countries
(25,000 and 39,000) define a range that depicts the likely
uncertainty of the estimates that arises from the lack of detailed
data for visitors who fly here on nonqualifying airlines. 

There is a specific logic for using the two alternative assumptions. 
That is, the known quantity for each sending country and airline is
the number--or percentage--of unrecorded departure forms.  If the
percentage of unrecorded departure forms is higher for passengers on
"nonqualifying" airlines than for passengers on "qualifying" airlines
(as is the case for Mexico, for example), this difference is likely
attributable either (1) to the fact that system error is higher for
nonqualifying airlines (whereas equal overstay rates apply for
passengers on both groups of airlines) or (2) to the fact that the
overstay rate is higher for the nonqualifying airlines (whereas the
same rate of system error applies) or (3) to some combination of
higher system error and higher overstay rates for the nonqualifying
airlines.\26 A range of estimates based on our two alternative
assumptions covers these three possibilities.\27 For each country,
the size of the range is determined by the empirically observed
difference between the rates of unrecorded departure forms for
qualifying and nonqualifying airlines. 


--------------------
\24 Specifically, our overstay estimate of 24,742 for the nine
sending countries, based on assumption 1, is 47-percent lower than
INS' estimate of 46,864.  By contrast, our estimate for the same nine
countries based on assumption 2 (39,265) is 16-percent lower than
INS' estimate of 46,864. 

\25 It may be more plausible to assume equal overstay rates for
passengers from the same country than to assume equal rates of
uncounted departures (system error) for passengers on the two types
of airlines ("qualifying" airlines for which separate estimates are
possible and "nonqualifying" airlines for which separate estimates
cannot be made).  Assuming equal rates of uncounted departures
(system error) seems less plausible because (1) the airlines are
responsible for collecting the forms and sending them to INS, and (2)
as shown in table I.2 in appendix I, rates of system error vary
across airlines--even for passengers from the same index country. 

\26 For cases where the percentage of unrecorded departure forms is
lower for nonqualifying airlines (for example, Germany), analogous
logic applies.  That is, the lower rates are likely to be explained
by lower system error, lower overstay rates, or some combination of
these two. 

\27 Notably, however, the range does not include the possibility that
where the percentage of unrecorded forms is higher, either system
error or overstay rates could be lower. 


      LIMITATIONS AND POTENTIAL
      IMPROVEMENTS
---------------------------------------------------------- Letter :4.4

All overstay estimates require some assumptions--and are therefore
subject to some degree of uncertainty.  At the time we drafted this
report, the only estimates other than those that we made were INS'
estimates based on its global approach.  The method we developed
reduces the uncertainty relative to INS' global approach because the
assumptions are more limited.  However, it is important to realize
that even the range for airline-by-airline estimates described above
does not take account of all sources of uncertainty.  There is
variation in system error across index countries--even for passengers
on a particular airline.  And it is certainly possible that, even on
a particular qualifying airline, system error might be higher (or
lower) for passengers from sending countries (for example, the
Bahamas or Mexico) than it is for passengers from index countries.\28

Although we believe the procedures we devised are a step in the right
direction, we also believe further improvements are possible.  In
responding to an oral briefing on our work, INS officials agreed that
our method constitutes a step forward, and they suggested
modifications that build upon--and that they believe might
improve--our approach.  Specifically, INS suggested increasing the
number of index countries and using more detailed data on variation
in system error by port of entry.  Other expert reviewers provided a
variety of suggestions, including using more complex models and
conducting special studies to obtain empirical estimates of system
error in nonindex countries.\29


--------------------
\28 Since differences in system error do exist for passengers from
different index countries even when traveling on the same airline, it
is likely that system error for individual sending countries differs
from the index countries' estimate to some degree.  And there is no
way of knowing, at present, whether the differences occur about
equally in each direction (and so would tend to balance each other,
on average, worldwide) or whether they are predominantly in one
direction. 

\29 See pp.  38-40 for examples of the kinds of empirical studies
that might be appropriate. 


   RECOMMENDATION TO THE
   COMMISSIONER OF INS
------------------------------------------------------------ Letter :5

We recommend that the Commissioner of INS have new overstay estimates
prepared for air arrivals from all countries, using improved
estimation procedures such as those discussed in this report,
including, as appropriate, the potential improvements suggested by
INS or by reviewers of this report. 


   AGENCY COMMENTS
------------------------------------------------------------ Letter :6

INS agreed that data on the individual airlines could improve its
estimates of overstays.  INS developed a new version of the
airline-by-airline approach and revised its criteria for selecting
index countries--replacing its "original" set of index countries with
a new set of 17.  In its written comments, INS compared estimates
obtained with its old and new estimation procedures.  \30

INS concluded that (1) the two methods produced differing estimates
for certain countries, and (2) the worldwide estimate of overstays
obtained with its new procedures (104,000 for the visitor category
and time period in question) essentially matched the number estimated
with its old procedures (107,000).  More recently, INS told us that
it will no longer use its previous approach and has adopted the
airline-by-airline method (including the corrected estimation
formula). 

By adopting an airline-by-airline approach and correcting its
formula, we believe INS has taken an important step forward.  This is
partly because achieving more accurate estimates of overstays from
individual countries is essential for certain policy-related
decisions--particularly those involved in administering the Visa
Waiver Pilot Program.  In addition, contrary to INS' conclusion, we
believe that the agency's change to an airline-by-airline method may
make a substantial difference in the worldwide estimate.  As we
explain in appendix II, depending on which sets of index countries
INS uses, the worldwide overstay estimate achieved with
airline-by-airline procedures may be 17- to 25-percent lower than the
global estimate.  (See pp.  56-58.)

Although INS' adoption of an airline-by-airline method is an
important step in the right direction, we believe the improvement of
overstay estimation methods is a "work in progress." As discussed in
appendix II, we believe INS' selection of index countries deserves
further study.  Also, certain aspects of INS' airline-by-airline
procedures differ from those that we used, and we have some
potentially important concerns about those differences.\31 Finally,
the experts who reviewed a draft of this report suggested possible
strategies for reducing the uncertainty that characterizes both our
estimates and INS', but INS has not had an opportunity to consider
the experts' suggestions.\32 For these reasons, we believe our
recommendation to the Commissioner of INS is still appropriate. 

As agreed with your office, unless you publicly announce its contents
earlier, we plan no further distribution of this report until 30 days
from its date of issue.  At that time, we will be sending copies of
this report to the Immigration and Naturalization Service, the
Department of State, and other interested parties.  We will also make
copies available to others upon request. 

If you or your staff would like to discuss any of the issues we
present here, please call me at (202) 512-2900 or Judith A. 
Droitcour, who served as project director on this study, at (202)
512-5885.  Other major contributors to this report are listed in
appendix IV. 

Sincerely yours,

Joseph F.  Delfico
Acting Assistant Comptroller General


--------------------
\30 The full text of INS' comments and our detailed response are in
appendix II. 

\31 See pp.  59-60. 

\32 See pp.  38-42 for the experts' suggestions. 


TECHNICAL APPENDIX
=========================================================== Appendix I

This appendix presents detailed information on the following
technical topics:  (1) the estimation of "system error" (percentage
of uncounted departures) and INS' "global" assumption that the level
of system error is the same worldwide (across all airlines and all
countries of citizenship); (2) the formula we developed for
estimating overstays (given an estimate of system error) and an
explanation of the error we identified in INS' computation formula;
and (3) a new set of procedures for estimating overstays that, by
incorporating data on specific airlines, avoids the need for INS'
global assumption and, at the same time, uses the correct computation
formula and appropriately weighted data.  Additional sections of this
appendix discuss (4) possible further improvements in estimation
procedures and (5) problems with overstay estimation procedures for
visitors arriving by land. 


   BACKGROUND
--------------------------------------------------------- Appendix I:1

Each year, millions of foreigners legally enter the United States as
"nonimmigrant" visitors (that is, on a temporary basis and for a
specific purpose, such as tourism).  The INS Nonimmigrant Information
System tracks records of legal nonimmigrant visitors by country of
citizenship; visa category (tourist visit, business, or other purpose
such as temporary work); mode of travel (air, land, or sea); and for
each air passenger, the airline on which he or she entered the United
States.\1 As indicated by the NIIS data, the large majority of
foreign visitors are tourists who enter by air.  (It is important to
note that many Canadian visitors are not counted by this system.  The
same is true for many Mexican visitors who use border-crossing
cards.\2 Data on foreign students entering the United States to
attend school are maintained in a separate system and are not part of
the estimates discussed in this report.)

INS also attempts to determine whether or not each foreign visitor
(identified by name, date of birth, country of citizenship, and
passport number) exits the United States by 9 months after his or her
expected date of departure.  INS' use of a minimum 9-month overstay
period for purposes of calculating the overstay estimates discussed
in this report means that transients who overstayed for only a few
weeks or months are not included in these figures.  Rather, INS
defines estimated overstays as foreign visitors who--having been here
for a year or more--appear to have settled in the United States.\3
However, as explained below, there is (1) considerable error in
counting visitor departures and thus (2) uncertainty in the
estimation of overstays. 

Briefly, when a foreign visitor legally enters the United States, he
or she fills out an arrival/departure form (I-94 form; see figure
I.1).\4 The arrival portion of the I-94 form is detached and retained
by INS.  The departure portion of the form is stapled to the
visitor's passport.  Each visitor is supposed to turn in the
departure portion of the form when exiting the United States.  The
INS data system attempts to match the arrival with the corresponding
departure portion of the form.  Thus, it is possible to determine the
number of foreign visitors for whom departure forms have not been
recorded ("unrecorded departure forms"). 

In some instances, unrecorded departure forms correspond to visitors
who overstayed.  Often, however, departure forms have gone unrecorded
because either (1) the forms were not turned in, not collected, or if
collected by an airline, not returned to INS; or conceivably, (2) the
forms were returned to INS but not correctly recorded as of a 9-month
period following the expected departure date. 

   Figure I.1:  Arrival/Departure
   Form I-94 for Foreign Visitors
   to the United States

   (See figure in printed
   edition.)

   Source:  Immigration and
   Naturalization Service.

   (See figure in printed
   edition.)


--------------------
\1 The NIIS data system includes a record of information that
visitors provide on arrival/departure forms, including sex, age, and
so forth; port of entry is also recorded in the data system.  We note
that an unknown number of persons fraudulently enter this country as
tourists.  If the fraud is successful, the record of such a person's
seemingly legitimate entry would be tracked together with legal
entries in the NIIS system. 

\2 For Mexicans with border-crossing cards, travel is limited to an
area within 25 miles of the U.S.-Mexican border for periods no longer
than 72 hours. 

\3 For example, a tourist with a 3-month visa who overstays for 9
months has been in the United States for a year.  Note that the
procedures described here estimate the number of new illegal
immigrants who are overstays.  Certain analyses transform these
estimates to estimates of the number of illegal immigrants--living
here as of any one date--who initially came in legally and
overstayed.  To perform this transformation, it is necessary to
estimate the number of overstays who returned to the home country
before the date in question, the number who adjust to a legal status
before that time, and so forth. 

\4 Visitors from countries in the Visa Waiver Pilot Program use form
I-94W.  The current Visa Waiver Pilot Program countries are Andorra,
Austria, Belgium, Brunei, Denmark, Finland, France, Germany, Iceland,
Italy, Japan, Liechtenstein, Luxembourg, Monaco, Netherlands, New
Zealand, Norway, San Marino, Spain, Switzerland, Sweden, and United
Kingdom.  Effective April 1, 1995, Ireland was also designated as a
pilot program country, but with probationary status. 


   SYSTEM ERROR
--------------------------------------------------------- Appendix I:2

The fact that many visitors who actually leave the United States are
not on record as having departed constitutes a major problem for
overstay estimation.  For air passengers, the airlines have been
charged with collecting departure forms and transferring these to
INS.  The agency plans to begin a new airline data collection effort
soon; while INS characterizes this effort as still "in the design
phase," it may have some potential for improving INS air departure
data.  One other possible--but likely expensive--solution would be
for INS officials to collect departure forms at airports.\5 For land
travelers, the key reason why departure records are missing is that
roadways exiting the United States lack facilities for collecting
departure forms.\6

Although uncollected I-94 departure forms seem to be the chief
problem, some portion of uncounted departures may possibly result
from other factors, such as the loss of forms after they have been
collected, incorrect keypunching (which can prevent a match between
entry and exit forms), or inadvertent deletion of information from a
computer file.\7

INS uses the term "system error" to refer to uncounted departures. 
Estimates of system error are not negligible and seem quite large
relative to the number of overstays.  Yet no one knows, with any
precision, how large the system error component is.  Consequently,
any estimate of overstays is necessarily somewhat uncertain. 

The estimation problem can be briefly described as follows.  As shown
in figure I.2, the three major known quantities in the INS
Nonimmigrant Information System are

  -- the total number of expected departures, that is, the number of
     departures that should occur by the time the visitors' legal
     periods of stay (plus the subsequent 9-month period) have
     expired;

  -- the number of counted departures, that is, the number of foreign
     visitors who turned in departure forms that were received and
     correctly recorded and stored by INS;\8

and

  -- the difference between expected departures and counted
     departures, which we term "unrecorded departure forms."

   Figure I.2:  Known Quantities
   in INS Data on Foreign Visitors

   (See figure in printed
   edition.)

In sum, the estimation challenge is that the "unrecorded departure
forms" category includes both those foreign visitors who failed to
depart (overstays) and those who did depart but were not counted as
having departed (uncounted departures or system error).  The data do
not indicate how many foreign visitors with unrecorded departure
forms fall into each of these two groups.  It is clear, however, that
being able to estimate the number of uncounted departures (system
error) would allow the number of overstays to be estimated. 


--------------------
\5 We have not reviewed INS data collection plans in detail and
therefore cannot comment on the likelihood that they will actually
result in improved overstay information in the coming years.  A bill
sponsored by the Chairman, House Subcommittee on Immigration and
Claims, would "establish a pilot program in which officers of the
[INS] collect a record of departure for every alien departing the
United States and match the records of departure with the record of
the alien's arrival in the United States." (Title I, sec.  113, of
H.R.  2202, 104th Cong., 1st sess.) The pilot program would be
operated "at no less than 3 of the 5 air ports of entry with the
heaviest volume of incoming traffic from foreign territories" and
would provide indications of the cost of such a program nationwide. 

\6 See the section on land entries on pp.  42-43. 

\7 INS recognizes that system error includes lost departure forms,
inadvertent keying errors, and errors resulting from the fact that
some extensions of stay are not entered into the NIIS data system. 
According to INS, a contractor currently keypunches the number on the
arrival form, although departure forms are scanned.  Some NIIS data
were lost for fiscal year 1990 because of a computer error; only
indirect estimates of overstays are therefore possible for fiscal
year 1990 (although these limitations were not noted by INS in
publications of overstay estimates).  Other errors have been detected
in fiscal year 1993 and 1994 data, and they are currently not usable
for making overstay estimates.  Errors that preclude the use of all
data for certain fiscal years are conceptually distinct from the
"system error" that pervades the data that must be used to obtain
overstay estimates.  Nevertheless, the fact that the larger errors
occur alerts one to the possibility of substantial numbers of smaller
computer errors in the data set.  Although we did not collect
information on "nonmatches" (departure form records that could not be
matched to arrivals), we note that such information might inform the
estimation procedure. 

\8 Although the number of counted departures is taken as known, some
uncertainty may pertain to this category.  That is, some overstays
(such as those who had entered with fraudulent documents or who had
fraudulently obtained valid documents) might find a way to turn in
their departure forms in order to create the impression that they had
left--when in fact they had not. 


      INS DEVISED A STRATEGY TO
      ESTIMATE SYSTEM ERROR
------------------------------------------------------- Appendix I:2.1

INS devised a creative strategy to estimate system error.  The key is
to examine the rates of unrecorded departure forms in "index"
countries--such as Australia, Sweden, Finland, and Switzerland--for
which INS believes it is safe to assume that there are only
negligible numbers of overstays.\9 If this is so, then for visitors
who are citizens of these (index) countries, the rates of unrecorded
departure forms and the rates of uncounted departures (or system
error) would, for all intents and purposes, be equal.\10

Initially, INS defined 12 index countries:  Australia, Belgium,
Finland, Kuwait, Netherlands Antilles, New Zealand, Norway, Saudi
Arabia, Singapore, Suriname, Sweden, and Switzerland.  Later, Kuwait
was dropped from the list (because of overstays resulting from the
Gulf war).\11 INS reported that the 12 countries were selected
according to five criteria, one of which is low rates of unrecorded
departure forms.\12

INS realized that the data for foreign visitors from the index
countries provide a potential window onto the level of system error
that occurs in other countries.  INS applied this strategy separately
for visitors who arrived by air, land, and sea.  This approach
involves an assumption that travelers who arrive by one mode of
transportation generally depart by the same mode--for example, that
visitors who arrive by air generally depart by air.  This may be less
likely for citizens of certain countries.  Notably, Mexicans and
Canadians who arrive by air may be more likely to depart by land than
visitors from countries that do not border the United States. 


--------------------
\9 See Robert Warren, "Annual Estimates of Nonimmigrant Overstays in
the United States:  1985 to 1988," in Frank D.  Bean, Barry
Edmonston, and Jeffrey S.  Passel, Undocumented Migration to the
United States:  IRCA and the Experience of the 1980s (Washington,
D.C.:  Urban Institute Press, 1990), pp.  77-110. 

\10 To the extent that visitors from index countries do overstay,
system error would be overestimated.  As one reviewer of this report
pointed out, some visitors from index countries may be "technical
overstays" in that if they had applied for visa renewal or other
legal status, it probably would have been granted.  This means that
estimates of system error may include some "technical overstays." If
rates of "technical overstays" are the same for index and nonindex
countries, then rates of system error estimated for nonindex
countries encompass the technical overstays.  Such persons would be
included in rates of system error rather than being counted as
overstays (in the estimates presented in this report).  However,
because rates of technical overstays may differ across countries,
this represents a source of uncertainty in all current estimates. 

\11 In the sample data that INS provided to us for calculating
airline-by-airline estimates, Saudi Arabia was not included. 
Therefore, in our trial estimates of the new procedures--and in the
comparison estimates that we subsequently asked INS to provide to us
based on the agency's usual procedures--both Kuwait and Saudi Arabia
were omitted from the set of index countries. 

\12 The other criteria are "(1) low backlogs for immigrant visas; (2)
low numbers of applicants for legalization; (3) low numbers of alien
apprehensions by the INS; (4) low estimates of undocumented aliens
counted in the 1980 Census" (Warren, 1990). 


      INS CALCULATED SYSTEM ERROR
      FOR ALL AIRLINES GROUPED
      TOGETHER
------------------------------------------------------- Appendix I:2.2

Using the index country data for visitors who arrived by air, INS
calculated a single estimate of system error that combined data for
all index countries' air passengers and the airlines they used to fly
into the United States.\13 By calculating a single rate of system
error--and applying it globally--INS procedures assumed that this
"single point estimate of system error applies to every country of
origin within a particular category of admission." (Warren, 1990, p. 
81.) An INS official noted that "it is possible that some areas of
the world have different rates of system error.  For example, some
airlines might do a better job of emphasizing the collection of I-94
departure forms." (Warren, 1990, p.  81.)

In fact, certain index countries and airlines appear to be
considerably more assiduous in collecting departure forms than
others.  Given this fact, INS' approach rests on assuming that the
rate of system error estimated on the basis of index countries' air
passengers (and the airlines that they use to fly into the United
States) is, on average, at least reasonably representative of system
error for air passengers from other countries--and the different
airlines that they may use to fly into the United States.  Of course,
no data exist to show whether system error is the same or different
in index countries and in other (nonindex) countries; this lack of
data represents the major source of uncertainty in current overstay
estimates. 

The implications of using a global estimate of system error--as
opposed to an airline-by-airline approach--are as follows.  If the
"typical airline" serving the index countries (that is, serving
Australia, Switzerland, and so forth) is more assiduous in collecting
departure forms than the typical airline serving a given nonindex
country (for example, India), then system error is actually lower for
the airlines serving the index countries than for the airlines
serving India.\14 But the INS procedures would not account for this,
so system error would be underestimated for India (or an analogous
sending country).  Consequently, INS' estimated number of overstays
for India (or an analogous country) would be too high.  The logical
converse could also be true in some instances. 

Because the airlines collect the forms, we believe they are a key
factor in estimating system error.  But various other factors may
also play a role in determining the rate of system error for visitors
from a particular country.\15


--------------------
\13 Separate calculations were made for tourists and business
travelers and for air, land, and sea arrivals.  In these
calculations, INS weighted data for each index country equally
(rather than according to the numbers of visitors). 

\14 We refer here to the potential difference between the rate of
uncounted departures for visitors from index countries (that is, the
average taken across those countries) and the rate of uncounted
departures for visitors from the sending country. 

\15 For some countries, system error is likely to be different than
for most other countries.  For at least two reasons, system error may
be higher for Mexico and Canada than for other countries.  First, as
previously noted, Mexicans and Canadians who arrive by air may be
more likely to depart by land than air arrivals from index countries
(which do not border the United States).  Because system error is
much higher for land departures, INS' estimate of system error for
air arrivals from Mexico may underestimate of the true level of
system error characterizing Mexican air arrivals.  Second, the
airlines' collection of departure forms may be more lax on flights to
Mexico and Canada because regulations do not require collection of
departure forms for foreign visitors making short "side trips" to
Mexico or Canada during a longer visit in the United States.  These
considerations suggest that overstays might be overestimated for
Mexico and Canada.  The reason is that underestimates of system error
translate directly to overestimates of overstays.  (A somewhat
similar situation might apply for visitors who arrive by air from one
or more Caribbean nations because they may be more likely to depart
by sea than visitors from index countries.)


      INS USED THE AVERAGE PLUS
      ONE STANDARD DEVIATION
------------------------------------------------------- Appendix I:2.3

INS calculates its "global" estimate of system error by taking the
average percent of unrecorded departures across the 11 index
countries plus the standard deviation of the 11 numbers.\16 (See
table I.1.) INS adds one standard deviation to the average in order
to avoid underestimating system error.\17 Adding an adjustment of
this sort seems to be justified because one criterion INS used to
select the index countries was low rates of unrecorded departure
forms.  The fact that INS used this criterion means that the index
countries may not only have zero (or near-zero) rates of overstays,
but they may also have lower-than-average rates of system error.  We
believe, as INS does, that adding an adjustment may help to correct
this possible bias.  However, we have not assessed the adequacy of
this corrective factor. 



                               Table I.1
                
                   INS' Computation of System Error\a

                                                                Percen
                                                                  tage
                                                                appare
                                                                    nt
                                                                overst
Country of citizenship                                              ay
--------------------------------------------------------------  ------
Australia                                                         8.09
Belgium                                                          10.21
Finland                                                           5.71
Kuwait\b                                                          8.65
Netherlands Antilles                                              9.60
New Zealand                                                       7.92
Norway                                                            9.06
Saudi Arabia                                                      8.36
Singapore                                                         5.79
Suriname                                                          7.91
Sweden                                                            8.81
Switzerland                                                       8.14
----------------------------------------------------------------------
Note:  Mean apparent overstay (average unrecorded departure forms): 
8.19%; standard deviation:  1.33%; and estimated system error: 
9.52%. 

\a Tourist air arrivals, October 1986-March 1987.  INS calculated the
mean with each country (large or small) given an equal weight. 

\b Kuwait was later dropped from the list of index countries (because
the Gulf war increased the number of overstays), yielding 11 index
countries. 


--------------------
\16 In these calculations, INS takes a simple, rather than a
weighted, average.  That is, INS gives large and small index
countries equal weight. 

\17 For the example shown in table I.1, this procedure produced an
estimate of system error of 9.52 percent--that is, 8.19 percent rate
for unrecorded departure forms in the index countries plus 1.33
percent representing the standard deviation. 


   SYSTEM ERROR VARIES
--------------------------------------------------------- Appendix I:3

We believe a main limitation of the INS estimator is its global
quality.  That is, INS calculated one estimate of system error based
on the airlines that index country passengers flew to enter the
United States--and used this estimate for all sending countries and
all airlines that citizens of the sending countries flew.  But system
error is not constant. 

Examining index country data for one 6-month period, we found that
the rate of unrecorded departure forms, which INS takes as the rate
of uncounted departures in index countries, varies across airlines as
well as across countries.  (See table I.2.) Dividing the airlines
into two groups--those with generally lower levels of system error
and those with higher levels--it is apparent that the airlines with
lower levels of system error tend to be based in index countries,
mainly Australia and New Zealand or northern European countries.  By
contrast, those airlines with higher levels of system error are--in
the majority of cases--American carriers based in the United States. 



                                    Table I.2
                     
                       Variation in Percentage of Uncounted
                      Departures (System Error) for Selected
                                Index Countries\a


                         New
Qualifying    Austra  Zealan  Belgiu  Finlan  Singapor                  Switzerl
airline          lia       d       m       d         e  Norway  Sweden       and
------------  ------  ------  ------  ------  --------  ------  ------  --------
Lower levels
 of system
 error
Air New 2      .4% 3     .2%
 Zealand-
 Int.
Air New 2       .9 3      .5
 Zealand
KLM Royal                       3.5%                              4.6%
 Dutch
Qantas           4.3     4.9                                       4.0
Icelandair                                                2.3%     5.7
Singapore 5       .4                       3       .1%
 Airlines
SAS                                3     .3%               4.4     5.2
 Scandinavian
Finnair                                  2.6                       8.4
Higher
 levels of
 system
 error
Air Link                                 4.6               4.9     7.3
 Corp.
American 4      .4 4      .8     5.8                               6.8      7.3%
 Airlines
United           4.5     5.1                       8.0
 Airlines
Delta            4.9                                                         7.0
British          4.1     3.3             7.4               7.5     9.1       8.1
 Airways
Air              6.0     6.1                                       6.7       8.3
 Micronesia
Pan American     5.8     6.1     7.2     6.0               9.6    10.6      13.1
Virgin           8.7     9.1
 Atlantic
Northwest                                  4        .9       1     3.5
 Orient
TWA              6.8            14.1                      12.9    19.1      18.5
--------------------------------------------------------------------------------
\a Based on tourist air arrivals from October 1990 to March 1991. 
Data are provided for cells representing 1,000 or more passengers. 
The table includes only those index countries with 1,000 or more
passengers on each of two or more airlines and only those qualifying
airlines with 1,000 or more passengers from each of two or more
countries.  It shows variation across countries for a given
airline--and variation across airlines for a given country (for cells
in which reasonably reliable estimates of system error can be made). 

Further consideration indicates that, when flying between the United
States and other countries, airlines in the group with lower levels
of system error generally tend to fly mainly between the United
States and Australia, New Zealand, or northern European countries. 
By contrast, the airlines with higher levels of system error not only
fly from index countries to the United States, but also serve many
other countries around the world (for example, countries in Latin
America or Asia), bringing travelers from these diverse regions to
the United States.  On a worldwide basis, these airlines with higher
system error would logically be more frequently used by visitors to
the United States than airlines in the other group. 

Potentially significant patterns like these suggest that, if an
estimation procedure could be based on the specific airlines that are
actually used by visitors from each foreign country, that procedure
might improve estimates of system error.  And improved estimates of
system error would reduce the uncertainty associated with overstay
estimates based on INS' global approach. 


   USING SYSTEM ERROR TO ESTIMATE
   OVERSTAYS
--------------------------------------------------------- Appendix I:4

INS uses its global system error figure to estimate the number of
overstays from each sending country.  In this section, we (1) present
a formula for estimating the number of overstays, given an estimate
of system error, and (2) contrast this formula with the INS
computation formula (in which we found an error). 

Figure I.3 provides the conceptual map needed to follow the ensuing
discussion.  Conceptually, expected departures may be divided into
true departures and overstays.  True departures can, in turn, be
divided into counted departures (that is, visitors whose returned and
recorded departure forms indicate that they have left the United
States) and uncounted departures.  The category of unrecorded
departure forms includes both overstays and uncounted departures.\18

   Figure I.3:  Conceptual Map for
   Estimating System Error

   (See figure in printed
   edition.)


--------------------
\18 The categories shown in figure I.3 may be applied to foreign
visitors in a specific visa category, arriving via a specific mode of
travel (air, land, or sea) from a particular sending country.  They
could also be applied to visitors arriving on a particular airline,
if an airline-by-airline approach were used. 


      TERMINOLOGY FOR COMPUTATIONS
------------------------------------------------------- Appendix I:4.1

As previously explained, the known quantities are: 

  -- the expected departures (EXD),

  -- the counted departures (CD), and

  -- the unrecorded departure forms (URDF) category, which is
     obtained by subtracting counted departures from expected
     departures. 

True departures (TD), overstays (OV), and uncounted departures (UCD
or system error) must be estimated. 

As discussed in the previous section, the purpose of estimating
system error using index countries' data is to estimate the
percentage and number of uncounted departures for every sending
country--and thereby to estimate the number of overstays.  But an
appropriate formula must be used. 

Two additional terms are needed for this discussion. 

  -- First, as mentioned above, true departures can be divided into
     counted departures and uncounted departures.  The symbol P
     refers to the true proportion of departures that are uncounted
     (that is, the true rate of system error).  Specifically,

     P = UCD/TD.

  -- Second, the symbol Pï¿½ refers to an estimate of system error (an
     estimate of P), defined as the average proportion of uncounted
     departures in the index countries plus one standard deviation. 
     Specifically,

     Pï¿½= Average (UCD/TD)i + SD,

where the subscript i denotes index countries and SD refers to the
standard deviation across the index countries. 

That is, the rate of system error (P) is estimated using index
countries' data.  Pï¿½ is an estimate of the proportion of true
departures that went uncounted.  As appropriate, P can be estimated
for all visitors arriving by air from all countries taken together
(using all data on passengers from index countries) or for some
subset of passengers such as those arriving on a specific airline
(using data on index countries' passengers who arrived on that
airline). 


      APPROPRIATE FORMULA AND INS
      ERROR
------------------------------------------------------- Appendix I:4.2

We derived the following formula to estimate overstays: 

     OV = EXD ï¿½ (CD/(1 ï¿½ Pï¿½))

Figure I.4 shows the derivation of this formula. 

   Figure I.4:  Estimating
   Overstays for Any One Country

   (See figure in printed
   edition.)

INS estimated overstays using the following incorrect formula: 

     OV = [(URDF/EXD) ï¿½ Pï¿½](EXD)

where OV refers to the overstay estimate for a sending country (visa
category and mode of travel), URDF refers to the number of unrecorded
departure forms for that country, EXD refers to the number of
expected departures for that country, and Pï¿½ refers to the estimated
rate of system error, based on the index countries data.  (See
Warren, 1990, p.  106.)

As shown in figure I.5, the incorrect INS formula reduces to

      OV = EXD ï¿½ CD ï¿½ Pï¿½(TD + OV)

           or

     OV = EXD ï¿½ CD ï¿½ Pï¿½(TD) ï¿½ Pï¿½(OV)

This result indicates that when INS subtracts out the number of
uncounted departures attributable to system error, it actually
subtracts out not only the proportion of true departures that went
uncounted, but also--wrongly--the same proportion of overstays. 
Assuming Pï¿½ is an adequate estimate of the rate of system error, the
effect of using the incorrect INS calculation formula shown here is
to underestimate the number of overstays.\19

   Figure I.5:  Explication of the
   Error in INS' Formula

   (See figure in printed
   edition.)


--------------------
\19 To illustrate, suppose there are 1,000 expected departures for a
country and 800 counted departures.  Further suppose that the
estimate of P (system error) is 0.10.  Using GAO's formula, we have
1,000 ï¿½ 800/(1 ï¿½ 0.10) = 1,000 ï¿½ (800/0.90) = 1,000 ï¿½ 889 = 111
overstays.  Using INS' incorrect formula produces a different result: 
1,000 ï¿½ 800 ï¿½ 0.10(1,000) = 1,000 ï¿½ 800 - 100 = 1,000 ï¿½ 900 = 100
overstays. 


   GAO METHOD FOR OVERSTAY
   ESTIMATION
--------------------------------------------------------- Appendix I:5

To obtain an estimate of overstays that takes advantage of INS data
on the specific airlines that foreign visitors from different
countries actually use, we developed the four-step approach described
below.  Three points regarding the assumptions made and not made by
our method are crucial: 

  -- First, our method does not assume that a single estimate of
     system error characterizes each country of the world, regardless
     of which airlines are used.  It does assume that the separate
     level of system error estimated for each airline that serves one
     or more index countries (for example, American Airlines, Delta,
     or British Airways) is about the same for passengers from index
     countries and for passengers from each nonindex country.\20

  -- Second, our method does assume that system error can be
     adequately described by the airline of entry to the United
     States.\21

  -- Third, with respect to nonqualifying airlines, which do not
     serve index countries, our method does require that an
     assumption be made.  Specifically, we used two alternative
     assumptions as follows:  We developed one set of estimates based
     on the assumption that for visitors from a particular sending
     country (for example, India), the overstay rate is the same for
     (1) passengers entering the United States on qualifying
     airlines, such as American Airlines or Delta, which serve one or
     more index countries, and (2) passengers entering the United
     States on other (nonqualifying) airlines.  We also developed a
     second set of estimates based on the very different assumption
     that--again for visitors from a particular sending country--the
     rate of system error is the same for (1) passengers entering the
     United States on qualifying airlines and (2) passengers entering
     on nonqualifying airlines.  (Essentially, where it was not
     possible to use information on the specific airline, we turned
     to available information on the specific country.)

Three caveats are appropriate:  First, there is variation in system
error across countries--even for a given airline (refer to table I.2
on p.  25); thus, it is possible that, even for a specific airline,
system error may be different for passengers from index countries and
from nonindex countries (either individual nonindex countries or
nonindex countries in general).\22 Second, there is not a perfect
correlation between the airline upon which a passenger enters and
departs from the United States; and in fact, logic suggests that for
Mexico and Canada, air passengers may be more likely to depart by
land than would air passengers from index countries (since these do
not border the United States)--suggesting that system error may be
higher for citizens of Mexico and Canada than the levels that are
estimated using an index countries' methodology.\23 Third, overstay
rates--as well as rates of system error--may differ for travelers
from the same country who arrive on qualifying and nonqualifying
airlines.\24

Despite these caveats, we believe the assumptions we have made are
more plausible than the global assumption that INS made concerning
system error.\25 The four steps of the approach we devised are
described below and illustrated in table I.3. 



                                    Table I.3
                     
                       GAO's Airline-by-Airline Method for
                               Estimating Overstays


Visitors arriving on
qualifying airlines\a      Yes                        No
-------------------------  -------------------------  --------------------------
Yes                        Step 1: Estimate the rate  Step 2: Use step 1
                           of uncounted departures    estimates of uncounted
                           (system error) for each    departures (system error)
                           qualifying airline, using  together with the
                           data on visitors from      appropriate formula to
                           index countries who        estimate overstays among
                           entered the United States  visitors from each
                           on qualifying airlines.    nonindex country who
                                                      arrived on each qualifying
                                                      airline.

                                                      Step 3: For each nonindex
                                                      country:
                                                      (a) combine the step 2
                                                      overstay estimates for
                                                      qualifying airlines to
                                                      obtain the overstay rate
                                                      for visitors from that
                                                      country who arrived on
                                                      qualifying airlines; and
                                                      (b) combine the step 1
                                                      estimates of system error
                                                      for qualifying airlines to
                                                      obtain the rate of system
                                                      error for visitors from
                                                      that country who arrived
                                                      on qualifying airlines.

No                         Not applicable.\c          Step 4: For each nonindex
                                                      country:
                                                      (a) project the step 3a
                                                      overstay rate to visitors
                                                      from the same country who
                                                      entered the United States
                                                      on nonqualifying airlines,
                                                      which produces one set of
                                                      overstay estimates; and
                                                      (b) project the step 3b
                                                      rate of system error to
                                                      visitors from the same
                                                      country who entered on
                                                      nonqualifying airlines,
                                                      which produces a second
                                                      set of overstay estimates.
--------------------------------------------------------------------------------
\a Conceptually, qualifying airlines are defined as those that
regularly fly between at least one index country and the United
States.  Operationally, we defined qualifying airlines as those with
at least 1,000 passengers from a single index country in a 6-month
period. 

\b Visitors from index countries (such as Sweden and Switzerland) are
thought to include virtually no true overstays.  Data on visitors
from these countries are used to estimate rates of uncounted
departures, airline by airline.  The nine countries for which we
obtained overstay estimates are all nonindex countries.  (We note,
however, that INS does obtain overstay estimates for index as well as
nonindex countries.)

\c Data on visitors from index countries are not used to estimate
rates of uncounted departures for nonqualifying airlines. 


--------------------
\20 Specifically, we assume that for each airline of entry, the
weighted average of the percentage of uncounted departures for index
countries' passengers (plus one standard deviation) represents system
error for that airline worldwide. 

\21 This assumption is required because it is not possible to know
what airline a traveler's departure form was not counted on--or what
airline he or she did not depart on. 

\22 This is partly because variables other than the specific airline,
such as port of entry, may play a role in determining levels of
system error.  Also, travelers from certain countries may be more
proactive in turning in their departure forms than travelers from
other countries.  Factors such as these represent potentially key
sources of uncertainty in estimating overstays when using an index
countries' methodology. 

\23 As described in a later section of this appendix, there are no
facilities for collecting forms for land departures; therefore, the
rate of uncounted departures is much higher for land departures. 

\24 See p.  10 for a brief description of the interrelationship of
the two alternative assumptions we make for nonqualifying airlines. 
Also presented there is an explanation of why, when taken together,
these two alternative assumptions define the likely level of
uncertainty attributable to the fact that not all passengers arrived
on qualifying airlines. 

\25 Recall that our assumptions are limited to passengers traveling
on the same airline or to visitors from the same foreign country. 


      STEP 1
------------------------------------------------------- Appendix I:5.1

Using data on index countries' air passengers, we estimated system
error separately for each "qualifying airline." Conceptually, we
defined a qualifying airline as one (such as American Airlines,
Delta, British Airways, SAS, SwissAir, or Qantas) that regularly
serves one or more index countries--and has sufficient passengers to
allow a reasonably reliable estimate of system error for that
airline.  Operationally, we defined a qualifying airline as one that,
during the 6-month period we examined, carried at least 1,000
passengers from a single index country to the United States.\26 In
the sample data INS provided to us, we found that, according to our
operational definition, there were 29 qualifying airlines. 

To estimate system error for a specific qualifying airline, such as
American Airlines, we used the index countries' data for that airline
alone.  For example, to estimate PAA, we first calculated the
proportion of uncounted departures (system error) for each index
country--Australia (PAUS/AA), Switzerland (PSWZ/AA), Norway
(PNOR/AA), and so forth; then, we took the weighted average of these
figures.\27

To complete step 1, we also calculated the standard deviation of the
proportion of uncounted departures across index countries for a
specific airline.  We then took, as the estimate of system error for
a specific airline, the weighted average plus one standard deviation. 

Step 1 was repeated for each of the 29 qualifying airlines. 


--------------------
\26 For each qualifying airline, we used data from all index
countries.  Alternative operational definitions are, of course,
possible.  In selecting the level 1,000, we were mindful of the
following considerations.  First, the cutoff of 1,000 passengers
ensured sufficient data to support an estimate of system error for
each qualifying airline.  Second, given the set of 11 index countries
that INS had selected, the level of at least 1,000 passengers from a
single index country ensured that each qualifying airline probably
regularly served at least one index country, so that the data are not
likely to be anomalous.  The cutoff of 1,000 is appropriate, in part,
because of the size of INS' original set of index countries (Sweden,
Switzerland, and so forth).  Were INS to select much larger index
countries, a higher cutoff would probably be required to avoid
including airlines that do not regularly serve index countries. 

\27 In this way, an index country with few visitors using a
particular airline to enter the United States (for example, few
Australian visitors using SwissAir) would contribute only a small
amount to the estimate of P for that airline.  In other words, by
using weighted data, we avoided the "small cell problem."


      STEP 2
------------------------------------------------------- Appendix I:5.2

For a specific foreign country, such as Mexico, we estimated the
number of overstays who had come into the United States on each
qualifying airline.  That is, we estimated overstays for American
Airlines (OVMEX/AA), Delta (OVMEX/DEL), and so forth--performing the
overstay calculations for each of the 29 qualifying airlines that
transported Mexican visitors into the United States. 

There are two points to note with respect to these procedures. 

  -- First, within a particular sending country, the number of
     overstays who had arrived on each qualifying airline was
     estimated using the index countries' estimate of system error
     developed for that particular airline.  For example, in
     estimating OVMEX/AA, we used Pï¿½AA, and in estimating OVMEX/DEL,
     we used Pï¿½DEL, and so forth. 

  -- Second, in estimating OVMEX/AA, OVMEX/DEL, and so forth, we used
     the correct estimation formula specified in figure I.4: 

       OV = EXD ï¿½ (CD/(1 ï¿½ Pï¿½))

where Pï¿½ is the estimate of system error.  We applied the formula
separately for passengers traveling on each qualifying airline within
each sending country.  For example, to estimate Mexican overstays who
arrived in the United States via American Airlines, we used the
formula: 

     OVMEX/AA = EXDMEX/AA ï¿½ (CDMEX/AA/(1 ï¿½ Pï¿½AA))

Step 2 was repeated separately for each qualifying airline within
each country. 


      STEP 3
------------------------------------------------------- Appendix I:5.3

Step 3 includes two alternative procedures (steps 3a and 3b), each of
which is directed toward producing a separate set of estimates. 

In step 3a, we totaled estimated overstays across qualifying
airlines, within each country, and calculated the overstay rate for
passengers on all qualifying airlines in that country.  Specifically,
we divided the estimated total number of overstays who had arrived on
qualifying airlines by the total number of expected departures for
those airlines--again, for a particular country.\28

In step 3b, we calculated the rate of system error, within each
country, for visitors who arrived on qualifying airlines. 


--------------------
\28 These procedures are the equivalent of calculating a separate
overstay rate for passengers arriving in the United States on each
qualifying airline, within each sending country, and then taking the
weighted average of those rates across qualifying airlines. 


      STEP 4
------------------------------------------------------- Appendix I:5.4

Step 4 also has two components (steps 4a and 4b); again, each
component is directed toward obtaining a separate set of estimates. 

In step 4a, we projected the step 3a overstay rate to visitors from
the same country who entered the United States on nonqualifying
airlines.  In other words, we used the step 3a overstay rate as the
estimated overstay rate, that is, R(OV), for the entire country. 

Then, to obtain the estimated number of overstays for each country,
we multiplied the country-specific overstay rate times the total
number of expected departures for that country.  (The total number of
expected departures includes expected departures for visitors who had
arrived in the United States on qualifying airlines and for those who
had arrived on other, nonqualifying airlines.\29 ) This produced one
set of overstay estimates; expressed statistically, the number of
overstays for the k\th sending country (air arrivals) is estimated as
shown in figure I.6. 

In step 4b, we performed analogous procedures using rates of system
error rather than overstay rates.  This produced a second set of
alternative overstay estimates. 

   Figure I.6:  Statistical
   Expression of the New Overstay
   Estimator for Air Arrivals,
   Using Assumption 1

   (See figure in printed
   edition.)



--------------------
\29 We also performed a check at this point.  Specifically, we
compared the overstay estimate for each sending country to the number
of unrecorded departure forms for that country.  In all instances,
the estimated number of overstays was less than the number of
unrecorded departure forms.  (Logically, the overstay estimate must
be less than or equal to the number of unrecorded departure forms,
since the number of unrecorded departure forms--which is
known--includes both overstays and uncounted departures.)


   OTHER POSSIBLE NEW APPROACHES
--------------------------------------------------------- Appendix I:6

In response to our oral presentation of the new procedures, INS
suggested some additional possibilities for improved approaches to
estimating overstays.  Expert reviewers of a draft of this report
also made suggestions. 


      INS' SUGGESTIONS
------------------------------------------------------- Appendix I:6.1

One alternative approach would be a modification of the
separate-airlines procedures we presented above.  Specifically, INS
suggested an approach in which it would identify additional index
countries, thus expanding the number of "qualifying airlines." The
object (and benefit) would be to increase the percentage of
passengers from each sending country who arrive in the United States
on qualifying airlines.  In other words, the likely effect would be
to substantially reduce the number of persons for whom it would be
necessary to assume that the overstay rate (or, alternatively, the
rate of system error) is the same as on the qualifying airlines.  We
believe that increasing the number of index countries could be a
promising approach if appropriately implemented.  But the issue of
how to define specific criteria for index countries is a complex one
and has not been addressed in this report. 

Another approach that INS suggested would involve estimates of system
error that adjust for different ports of entry (for example, Miami,
New York, and so forth) as well as different airlines.  If this
approach proves practicable, it could also be used in conjunction
with adjustments for different airlines.  That is, airline and port
of entry could both be taken into account.\30


--------------------
\30 A log-linear analysis would allow simultaneous adjustments for
airline and port of entry, as well as other factors.  (For a
discussion of log-linear analysis, see Y.M.M.  Bishop, S.E. 
Fienberg, and P.W.  Holland, Discrete Multivariate Analysis:  Theory
and Practice (Cambridge, Mass.:  MIT Press, 1975).)


      EXPERTS' SUGGESTIONS
------------------------------------------------------- Appendix I:6.2

Other approaches or variations were suggested by expert reviewers,
including ideas for small-scale empirical studies, special analyses,
and complex estimation models. 


         EMPIRICAL STUDIES
----------------------------------------------------- Appendix I:6.2.1

Two experts suggested that it might be possible to conduct special
studies designed to estimate system error empirically.  Empirical
studies might consist of relatively small-scale data collections,
such as those used by the Bureau of the Census to estimate the
undercount in the decennial census.\31 Empirical studies may be
especially important for certain nonindex countries such those where
system error may be atypically high (for example, Mexico and
Canada),\32 those where the majority of visitors fly to the United
States on nonqualifying airlines, and so forth.  There are three
possibilities for empirical studies:  (1) "planted travelers"
studies, (2) follow-up studies of samples of visitors whose departure
forms were not recorded, and (3) airport surveys of passengers flying
out of the United States. 

A "planted travelers" study would utilize persons hired by INS as
"plants" who would exit the United States by air, using passports and
departure forms supplied by INS.\33 The agency could subsequently
check its data set to determine whether records of departure forms
for these persons were included.  Assuming that the planted travelers
were instructed to be passive rather than proactive in turning in the
forms, the results could be used to estimate a maximum rate of system
error for the airlines or countries in question.  Depending on the
number of planted travelers and the design of the study, system error
estimates could be obtained for selected countries, for the system as
a whole, or both. 

Another type of empirical study would be a "follow-up" study based on
a random sample of perhaps 400 unrecorded departure forms from a
specific country, airline, or other defined group.  These unrecorded
departure forms could be followed up in a number of ways, depending
on the country in question.  The initial follow-up in all cases could
consist of additional checks of INS records.\34 Then, for countries
that maintain records of reentering citizens or residents, it might
be possible to determine that, in some instances, the country of
origin's files contained a record of the traveler's return.  It also
might be feasible to attempt to contact individual travelers either
in their home country (after their return home) or in the United
States (if they overstayed).\35 Contacted persons might be asked a
few brief questions about trips in the past 2 years (airline used,
route flown, month of trip) as well as personal data (date of birth). 
The answers to the questions could be used to establish that the
correct person had, in fact, been contacted.  Random subsampling of
nonrespondents for further follow-up attempts might also be
appropriate.  Even though some unrecorded departure forms may remain
"unsolved," the percentage in question would, in all likelihood, be
greatly reduced.\36

If a general follow-back study of, for example, Mexican visitors
proved too difficult, it still might be possible to follow-back a
preselected subgroup, such as Mexican visitors aged 50 or older. 
This would be extremely useful if analyses of index countries' data
indicated either that (1) system error did not vary substantially
across age groups, or (2) system error varied across age groups
according to a reliable pattern. 

Yet another type of empirical study would involve surveying
passengers on selected flights departing the United States.  For
example, it might be possible for INS inspectors to check passports
immediately before passengers board.  This would reveal the number of
departure forms that were not collected by airline personnel.  Or, a
complete listing of departing visitors could be made and subsequently
compared to records in INS' data system.  Still other types of
empirical studies might be developed.  But the key point is that the
option of fielding small-scale empirical studies has the potential to
provide actual data on system error in nonindex countries.\37

Empirical studies might make it possible to avoid difficult
assumptions about system error in nonindex countries and about
nonqualifying airlines.  At a minimum, the data that these studies
could provide would greatly reduce the effects of possible bias on
the results. 


--------------------
\31 One expert pointed out that although a complete census of cases
(such as INS' Nonimmigrant Information System) can be useful
administratively, it may not be optimal for research purposes. 
Sample surveys--with a higher per-case cost--can provide higher
quality data than a census (for example, a lower rate of missing
information).  Because a relatively small number of cases are
involved, the total cost of sample surveys can be low relative to the
generalizable information that is provided. 

\32 As previously explained, visitors from Mexico and Canada who
arrive by air may depart by land, and system error is higher for land
departures.  Also, since I-94 forms are not collected for visitors
from other continents who are taking a short side trip to Mexico or
Canada, collection of other visitors' I-94 forms may be less complete
on flights from the United States to Mexico or Canada than on other
departing flights. 

\33 The idea for the planted travelers study was suggested by a
similar study that was aimed at assessing the undercount of the
homeless in the decennial census.  (See Kim Hopper, "Counting the
Homeless:  S-Night in New York," Evaluation Review, 16 (1992), pp. 
376-88.)

\34 For example, one check could be whether the individual has
applied for legal status in the United States; if so, he or she would
be categorized as an overstay.  Another would be whether he or she
reentered the United States before the time of expected departure. 

\35 A Department of State representative at the U.S.  Embassy in
Mexico City told us that the addresses of visa applicants are kept by
the U.S.  Department of State visa-issuing office for 1 year. 

\36 See National Research Council (U.S.) Panel on Census Requirements
in the Year 2000 and Beyond, Modernizing the U.S.  Census
(Washington, D.C.:  National Academy Press, 1995). 

\37 While this discussion has focused on studies in selected
countries, a global survey might also be possible.  If an empirically
based worldwide estimate of system error could be obtained, this
would provide a basis for an empirically based all-countries
estimate. 


         SPECIAL ANALYSES
----------------------------------------------------- Appendix I:6.2.2

The expert reviewers also pointed to various ways to utilize existing
INS data.  One analytic approach would be to look for a variable that
is not related to system error--but that might be related to
overstays.\38 Such a variable could form the basis of a new index. 
Suppose, for example, that system error does not vary across age.\39
Then, if it is possible to identify an age group with virtually no
overstays (one possible candidate would be persons over 50), persons
from that age group could be used as the index for their own country
and airline of arrival.  And still assuming that system error does
not vary across age groups, even if there were no particular age
group for which it could be assumed that overstays were virtually
nonexistent, a similar approach could nonetheless be used if
additional relevant data could be obtained.  That is, if an empirical
estimate of system error could be obtained for at least one age group
(for example, persons over 50) in a small-scale empirical study, this
estimate could be applied to other age groups.  (Refer back to the
discussion of empirical studies above.) Of course the variable, age,
is used here for illustrative purposes. 

Other analytic approaches were also suggested.  For example, when
frequent travelers reenter the United States, it is sometimes evident
that their previous departure forms were not collected.  (An analysis
of these cases might indicate a rate of uncounted departures that
would be considered a minimal rate if one believes that frequent
international travelers are more knowledgeable and proactive about
turning in their forms.\40 ) Estimates could be obtained separately
for different countries, airlines, or other subsets of visitors. 

Sensitivity analyses were also suggested as a way of examining a
variety of analytic options.  For example, as one expert emphasized,
negative estimates for specific airlines or countries occur when the
rate of unrecorded departure forms is lower than the estimated rate
of system error.  Both we and INS have reported these negative
estimates as zero overstays.  However, one reviewer suggested that
because a random component may influence these estimates, the overall
estimates should be calculated without converting negative numbers to
zero--thus reducing the number of overstays estimated when airlines
and countries are combined.  Whether issues like this are relatively
minor or might have a substantial impact could be explored in
sensitivity analyses. 


--------------------
\38 In building models to explain or predict system error, one would
look for variables--such as the specific airline--that are related to
system error; but another approach would be to check index countries'
data for variables for which system error does not vary. 

\39 In fact, this is an empirical question that can be examined
through index country data. 

\40 Another possibility might be to examine data on recorded
departure forms for which no arrival form could be found; these data
might be used to estimate the number of arrival forms that are
somehow lost or unrecorded even if turned in.  If optical scanning is
used in the future to record the arrival form number as well as the
departure form number, the estimate of lost or misrecorded arrival
forms could be used to estimate the corresponding number of lost or
misrecorded departure forms.  Balancing equations, analogous to those
commonly used in making demographic estimates of population changes
over time, might be useful in quantifying different components of
system error.  (Missing arrival forms might also be estimated by
counting "breaks" in the consecutively numbered arrival forms that
are recorded in INS' database.)


         ESTIMATION MODELS
----------------------------------------------------- Appendix I:6.2.3

In the absence of empirical studies such as those discussed above, a
more complex estimation model might improve on the airline-by-airline
method.  Indeed, instead of using only adjustments for airline of
arrival (as we did) or airline plus port of entry (a possibility that
INS suggested), experts pointed out that it is possible to adjust for
other background variables (for example, age and sex).  One reviewer
indicated that an optimal model would adjust for as many measured
variables as are relevant.\41 Another said that the model should
include enough variables to sufficiently account for variation in
system error across countries.  (As previously discussed, there is
variation in system error across countries--even for a specific
airline; refer to table I.2 on p.  25.)


--------------------
\41 See Roderick Little and Donald Rubin, Statistical Analysis With
Missing Data (New York:  Wiley, 1987), and Donald B.  Rubin, Multiple
Imputation for Nonresponse in Surveys (New York:  Wiley, 1987). 


   OVERSTAY ESTIMATES FOR LAND
   ENTRIES
--------------------------------------------------------- Appendix I:7

Within the INS data set being considered here, overstays who entered
the United States by land and sea are much less numerous than those
who entered by air.  However, a sizable number of Mexican visitors
enter by land--and for Mexicans, the estimated number of overstays
entering by land is not negligible.\42 System error is much higher
for land entries than for air arrivals because INS does not have
facilities for collecting the I-94 forms when visitors exit by land. 
Nevertheless, some I-94 forms are collected for persons who arrived
by land because (1) some visitors mail the forms in after returning
home or turn the forms in to a U.S.  embassy; (2) other visitors
reenter the United States, and the INS inspector collects the old
departure form at that time; and (3) still other visitors who arrived
by land depart by air. 

Estimates of overstays who arrived by land, like the air arrival
estimates, rely on estimates of system error based on unrecorded
departure forms for visitors from index countries.  Again, INS'
assumption is that a single estimate of system error, based on the
experience of visitors from Australia, Switzerland, and so forth,
applies to every sending country.  For the land entries that are
captured by NIIS (comprised chiefly of Mexicans), this seems
especially implausible to us.  (Specifically, INS assumes that the
experience of visitors from countries like Australia and Switzerland
who entered the United States by land is the same or at least similar
to that of Mexicans who entered the United States by land.)

The key issues in estimating overstays among land entries concern (1)
whether the system error estimates for foreign visitors from index
countries can fairly be applied to Mexican visitors arriving by land,
and more generally, (2) whether the lack of facilities to collect
departure forms when visitors exit by land means that overstay
estimation for land arrivals is ill-advised, given current methods
and data. 

One possibly troubling situation is that a number of tourists from
index countries may enter the United States from Mexico by land and
then fly home to Sweden, Switzerland, and so forth.  Such visitors
may comprise a relatively large proportion of the number of index
country visitors who arrive by land.  The possible result is that
index country visitors who arrive in the United States by land
may--in some fairly large proportion--depart by air.  If, by
contrast, Mexicans who enter by land generally also depart by land,
the use of the index country visitors' rate of system error would be
inappropriate.\43 Thus, the overstay estimates for land arrivals are
potentially misleading.  We realize that this argument is somewhat
speculative, but it highlights the possible need for improved
procedures for estimating overstays who did not arrive by air--and
illustrates the kinds of problems that might be assessed. 



(See figure in printed edition.)Appendix II

--------------------
\42 For example, during the 6-month period from October 1990 to March
1991, I-94 entry forms were processed for over 50,000 Mexican
tourists arriving by land--and INS estimated that more than 5,000 of
these persons became overstays.  Applying the correct computational
formula would raise this figure substantially. 

\43 Since the departure record has data fields for the carrier (and
flight number), it may be possible to empirically estimate the number
of land arrivals who were recorded as having departed by air. 


COMMENTS FROM THE IMMIGRATION AND
NATURALIZATION SERVICE
=========================================================== Appendix I



(See figure in printed edition.)



(See figure in printed edition.)



(See figure in printed edition.)



(See figure in printed edition.)



(See figure in printed edition.)

of INS' footnotes in this table, see our footnote 7 on p.  58. 



(See figure in printed edition.)



(See figure in printed edition.)



(See figure in printed edition.)



(See figure in printed edition.)



(See figure in printed edition.)



(See figure in printed edition.)


The following are GAO's comments on the June 22, 1995, letter from
the Immigration and Naturalization Service. 


   GAO COMMENTS
--------------------------------------------------------- Appendix I:8

INS told us that as a result of this report, the agency has changed
its procedures for estimating overstays.  Specifically, for foreign
visitors who arrive by air, INS has discontinued use of the old
"global" method and has adopted the airline-by-airline method.  INS
also told us that the error in its computation formula has been
corrected.  However, INS' written comments concluded that while the
airline-by-airline method may improve estimates for individual
countries, it produces a worldwide estimate that is "strikingly
similar" to its old worldwide estimate. 

We agree that by adopting an airline-by-airline approach, INS has
taken an important step forward; however, three major issues remain
concerning INS' new methods.  These are discussed in the following
three sections; a final section (pp.  61-62) responds to INS'
concerns about the estimates we presented in table 1. 


      DOES THE AIRLINE-BY-AIRLINE
      METHOD MAKE A DIFFERENCE IN
      THE WORLDWIDE ESTIMATE? 
------------------------------------------------------- Appendix I:8.1

The first issue concerns INS' conclusion that changing to an airline-
by-airline method makes essentially no difference in the worldwide
estimate.  Alternative INS calculations show that depending on the
index countries used, the airline-by-airline method produces a
worldwide estimate that is 17- to 25-percent lower than the
global-method estimate.  As discussed below, (1) the index countries'
methodology is potentially sensitive to the inclusion of even one
inappropriate index country; and (2) INS' global-method estimate and
its airline-by-airline estimate are based on different sets of index
countries--and each set may include an inappropriate index country. 
Specifically, we believe that Saudi Arabia and Japan may be
inappropriate index countries. 

Table II.1 shows the impact of removing Saudi Arabia and Japan from
the index countries INS used.  Of the two global-method estimates
shown in the first row of the table, we believe that 126,000 (the
estimate calculated without Kuwait and Saudi Arabia as index
countries) is the more valid figure.\1 The reason is that the index
countries' methodology assumes that each index country has virtually
no overstays.  INS originally selected 12 countries that met this
standard, but during the Gulf war, overstays apparently increased for
two of INS' original 12 index countries:  Kuwait and Saudi Arabia.\2
Given the time frame involved in the estimates examined here (October
1990 to March 1991), we believe INS would ideally have removed not
only Kuwait but also Saudi Arabia from its original set of 12 index
countries.\3



                               Table II.1
                
                 Worldwide Overstay Estimates, October
                           1990 to March 1991

                                        Estimates in   Other estimates
                                        INS' written     calculated by
INS method                                  comments               INS
----------------------------------  ----------------  ----------------
Global method                              107,000\a        126,000\\b
Airline-by-airline method                  104,000\c          96,000\d
----------------------------------------------------------------------
\a Based on 12 original index countries minus Kuwait.
\b Based on 12 original index countries minus Kuwait and Saudi
Arabia.
\c Based on 17 new index countries.
\d Based on 17 new index countries minus Japan. 

Of the two airline-by-airline estimates shown in the second row of
table II.1, we believe that 96,000 (the estimate calculated without
Japan as an index country) may be the more valid figure.  To
calculate its airline- by-airline estimates, INS selected a new set
of 17 index countries.  Kuwait and Saudi Arabia, among other
countries, were dropped, but several large countries were added,
including Japan.  We realize that INS' goal in selecting these
countries was to expand the set of qualifying airlines.  We agree
with this goal, but we question the inclusion of Japan. 

Japanese travelers have lower rates of system error than any other
index country on almost every airline for which a comparison can be
made.\4 Since index countries are used to estimate system error in
nonindex countries, our concern is that the Japan data may not fairly
reflect system error for passengers from nonindex countries.  (In
other words, using an atypical country as an index country can skew
results--even if there are no overstays from that country.) INS has
said in the past that, for this reason, Japan would not be
appropriate for use as an index country.\5 After the agency sent us
its written comments, INS recalculated "test estimates" using its
airline-by-airline procedures without Japan as an index country.\6

As summarized in table II.1, INS calculations show that had Saudi
Arabia been removed from the original set of index countries, INS'
worldwide global-method estimate for the Gulf war period examined
here would have been 126,000 rather than 107,000.\7 If Japan had not
been included in INS' new, larger set of index countries, INS'
worldwide airline-by-airline estimate would have totaled 96,000
rather than 104,000.  Substituting one or both of these estimates for
those that INS used would yield a very different conclusion: 
Specifically, the worldwide airline-by-airline estimate would be 17-
to 25-percent lower than the worldwide global-method estimate.  (That
is, 104,000 is 17 percent lower than 126,000, and 96,000 is 25
percent lower than 126,000.)

In light of the foregoing discussion, we believe that INS' conclusion
that the airline-by-airline method does not change the worldwide
estimate may be an artifact of (1) retaining an index country that is
inappropriate for the Gulf war time period and (2) selecting a new
index country that may be atypical and, thus, inappropriate. 
Therefore, we also believe that, before drawing general conclusions
about the effect of the airline-by-airline method, other worldwide
estimates that are not affected by these possible problems should
also be considered.\8


--------------------
\1 The global-method estimates totaling 126,000, which we presented
in our table 1 (on p.  8), were calculated for us by INS without
Kuwait and without Saudi Arabia as index countries. 

\2 For the time period in question, both Saudi Arabia and Kuwait
apparently failed to meet one of INS' stated criteria for selecting
index countries for use with its global method:  low rates of
unrecorded departure forms.  (The Saudi rate--9.1 percent--was higher
than that of any other index country and higher than the worldwide
average.)

\3 To assess whether trend figures would support this view, we
examined INS' worldwide overstay estimate for a 6-month period not
affected by the Gulf war--October 1986 to March 1987--and compared it
to alternative estimates for the time period examined in the report. 
(We chose the 1986-87 time period because a published INS estimate
was available; see Warren, 1990).  We found that worldwide, of all
tourists who arrived here by air, the percentage INS estimated to be
overstays was the same--2.2 percent--in both time periods provided
that both Saudi Arabia and Kuwait were dropped as index countries as
of the Gulf war.  But when INS kept Saudi Arabia as an index country,
the estimate decreased to 1.9 percent during the Gulf war time
period.  That is, consistent results were obtained when, as of the
Gulf war time period, both Saudi Arabia and Kuwait were dropped. 

\4 For example, on Northwest Orient, the rate of system error is 2.3
percent for Japanese passengers versus 4.9 percent to 13.5 percent
for other passengers; and on Air Micronesia, the rate is 3.6 percent
for Japanese passengers versus 6.0 to 8.3 percent for other index
countries' passengers.  (See table I.2 in appendix I.)

\5 When introducing an early version of its overstay estimation
strategy, INS stated that Japan's rates of system error were
"extremely low relative to all other countries of the world" and
"clearly do not represent overall system error." (Warren, 1986, p. 
653.)

\6 INS describes these new results as preliminary figures. 

\7 INS' table 1 (on p.  49) erroneously identifies the column labeled
"INS overstay estimates" as computed by GAO.  These estimates (which
total 126,000 worldwide) were calculated for us by INS--without
Kuwait and without Saudi Arabia as index countries.  (To further
clarify INS' table 1, we note that the next column is labeled
"Original INS estimates." These figures, which total 107,000
worldwide, differ from those in the column labeled "INS overstay
estimates" only in that Saudi Arabia was included as an index
country.  Also, to clarify a note in INS' table 1, INS' new set of 17
index countries was used only in calculating its airline-by-airline
estimates, which are shown in the column labeled "Revised INS
estimates" and total 104,000 worldwide). 

\8 Among the comparisons we believe would be relevant are estimates
for periods not affected by the Gulf war--for example, 1982 through
1988.  Comparisons for these years might indicate a difference of
approximately 17 percent, even with no change in index countries. 
Such comparisons would be particularly relevant because INS' earlier
paper on the size of the resident illegal immigrant population
(Warren, 1994) covers visitors who arrived from 1982 through 1991. 
The majority of these years were not affected by the Gulf war. 


      INS' AIRLINE-BY-AIRLINE
      PROCEDURES NEED FURTHER
      STUDY
------------------------------------------------------- Appendix I:8.2

The second issue concerning INS' new estimates arises because certain
aspects of INS' airline-by-airline estimation procedures (as we
understand them at this time) differ from our own.  We have some
concerns about these differences, and we believe that further study
is needed before INS presents its new overstay estimates as
definitive.  As just discussed with respect to INS' worldwide
estimates, INS' selection of Japan as one of its new index countries
may be inappropriate.\9 This points to a need for INS to continue
studying its criteria for selecting index countries.\10 As described
below, we also have concerns about other aspects of INS'
airline-by-airline procedures.  These include (1) INS' definition of
a qualifying airline and (2) the way that INS derives estimates for
those airlines that do not meet that definition. 

INS' definition of a qualifying airline is considerably more liberal
than the definition we used.\11 Unlike our definition, INS' includes
"home-country" airlines that do not fly between the United States and
any continent where an index country is located.  We agree that
expanding the number of qualifying airlines is an appropriate goal. 
However, stretching the airline-by-airline method (to cover such
airlines as A L Argentina, Lan Chile, Avianca, Mexicana de Aviacion,
and Aero Mexico) means relying on estimates that are driven by two
categories of index countries' travelers that we believe may be
atypical. 

The first category consists of European and Japanese members of the
international business community who reside in Latin America and
visit the United States as tourists.  Our concern is that this
category may consist mainly of experienced international travelers
who might be proactive in turning in departure forms.  And if they
visit the United States frequently (especially, if they reenter this
country within 9 months of the expiration of their initial visa),
then any uncollected departure forms--which should still be stapled
in their passports--would be collected by INS inspectors and
transferred to the INS database.  Relying heavily on this category of
index countries' travelers might, therefore, result in an
underestimate of system error for the home-country airlines in
question and a consequent overestimation of overstays. 

The second category consists mainly of European and Japanese tourists
on multilegged trips.  Our concern is that relying heavily on this
category of index countries' passengers might result in estimates of
system error for the wrong airlines.  The reason is that the
airline-by-airline approach necessarily assumes that the airline of
arrival is the same as the airline of departure.\12 But, when
compared to passengers with a simple round-trip itinerary, "world
travelers" on trips that cover three continents (for example, Europe,
the United States, and South America) seem more likely to depart the
United States on a different airline from the one on which they
arrived.  In fact, according to one expert, few airlines are licensed
for routes both (1) between Europe or Japan and the United States and
(2) between Latin American countries and the United States.  This
raises the possibility that INS' estimates of system error for
airlines like Avianca may, in fact, reflect rates for other airlines
(Lufthansa, Japan Air Lines, and so forth). 

Turning to INS' estimation of overstays among passengers arriving on
airlines it classifies as nonqualifying, we are concerned that,
whereas we used two alternative assumptions, INS used only one (our
assumption 2, as described in table 1 on p.  8).  Overall, of course,
only 5 percent of tourist air arrivals use airlines that do not
qualify under INS' liberal definition.\13

But that 5 percent may include citizens of countries marked by high
overstay rates, such as Poland.  Use of assumption 1 versus
assumption 2 could make a difference of roughly 2,000 overstays for
Poland.  We believe a range of estimates based on two alternative
assumptions might be more meaningful.  The need for such a range
would be most apparent for sensitivity analyses that omit certain
large index countries (such as Japan) or that use a stricter
definition of qualifying airlines. 


--------------------
\9 While the earlier discussion concerned worldwide estimates, we
note here that using Japan as an index country can have a dramatic
impact on overstay estimates for certain sending countries.  Notably,
by removing Japan as an index country, the overstay estimate for
Korea decreases from 2,100 to 1,300. 

\10 Until INS can adequately study the appropriateness of including
Japan as an index country, it would seem more prudent to present a
range of airline-by-airline estimates (calculated with and without
Japan as an index country) rather than present a single set of
estimates. 

\11 Whereas 29 airlines met our definition, INS stated that 89
airlines met its definition.  We defined a qualifying airline as one
that, during the 6-month period we examined, flew at least 1,000
citizens of a single index country to the United States.  INS defined
a qualifying airline as one that flew 1,000 or more total passengers
who are citizens of index countries to the United States.  For this
reason and also because INS' new set includes 17 index countries
(some of which are quite large), INS' definition is clearly more
inclusive than the one that we used. 

\12 This assumption is required because it is not possible to know on
which airline a traveler's departure form was not counted--or on
which airline he or she did not depart. 

\13 At least this is true when INS includes Japan as an index
country. 


      ADDITIONAL IMPROVEMENTS MAY
      BE POSSIBLE
------------------------------------------------------- Appendix I:8.3

The third issue is that some uncertainties are common to our
estimates and INS'--and that improvements aimed at reducing these
uncertainties may be possible.  For example, passengers from
seemingly typical index countries may not, in general, represent the
true level of system error for passengers from nonindex
countries--even when traveling on the same airline.\14 Another
example is that both we and INS converted negative overstay
estimates, which occur for several countries and airlines, to zero
overstay estimates.  However, because a random component may
influence these estimates, it might be preferable to calculate
combined-airline and combined-countries estimates without converting
the negative numbers to zero.  (See p.  41.) The effect of this
change would be to reduce the number of estimated overstays.\15

The special analyses, empirical studies, and more complex models
suggested by experts who reviewed this report could shed light on
these issues.  (See pp.  38-42.) But INS has not yet had an
opportunity to consider them.\16


--------------------
\14 The consistently low rate of unrecorded departure forms for
Japanese passengers highlights this possibility. 

\15 INS' new 104,000 worldwide estimate includes roughly 5,800
overstays from index countries (which supposedly have no overstays). 
This may be a result of converting negative numbers to zeros rather
than including them with positive numbers. 

\16 INS produced airline-by-airline estimates during the 30 days
provided for comment on a draft of this report, although we had not
suggested any time frame for INS to develop new estimation procedures
or new estimates. 


      INS' CONCERNS ABOUT OUR
      ESTIMATES
------------------------------------------------------- Appendix I:8.4

Our table 1 estimates for nine sending countries include a set of
estimates in which assumption 1 was used for passengers on
nonqualifying airlines.  That is, one set of our estimates is based
on the assumption that the same overstay rate characterizes (1)
passengers on airlines for which a separate estimate of system error
is possible (our qualifying airlines) and (2) passengers from the
same country who used other airlines.  In its written comments, INS
indicated it has empirical evidence that our assumption 1 is
incorrect, but did not present that evidence. 

We know of no direct way to check the assumption of equal overstay
rates for qualifying and nonqualifying airlines.\17

Thus, we presented a second alternative set of estimates for the same
countries, based on a very different assumption (assumption 2 in
table 1).\18 INS also questioned assumption 2.\19 However, when
assumptions 1 and 2 are used as the basis for alternative estimates,
there is a specific logic that we believe justifies the use of these
assumptions.  (See p.  10.)


--------------------
\17 We did examine three indirect indicators, including factors that
might affect a traveler's choice between a qualifying and a
nonqualifying airline.  Because a difference in fares might be
related, we compared current fares for qualifying and nonqualifying
airlines flying a number of international routes, and we found no
consistent differences.  Because some of the major qualifying
airlines are based in the United States, we confirmed that these
airlines (for example, Delta, United, and American) typically provide
bilingual flight attendants.  Finally, we found that INS inspectors
do not use the airline of arrival in profiles aimed at identifying
illegal aliens. 

\18 In the draft of this report, the estimates based on assumption 2
were reported in the text rather than in table 1. 

\19 Nevertheless, INS did use assumption 2 to derive overstay
estimates for the 5 percent of air passengers who arrived on airlines
it defined as nonqualifying. 


<>LIST OF EXPERTS
========================================================= Appendix III

The following experts in the fields of statistics and immigration
research reviewed a draft of this report and provided us with their
comments. 

Frank D.  Bean, Ph.D., Population Research Center, University of
Texas at Austin

Kenneth H.  Hill, Ph.D., Department of Population Dynamics, Johns
Hopkins University, Baltimore, Maryland

Demetrios G.  Papademetriou, Ph.D., Carnegie Endowment for
International Peace, Washington, D.C. 

Jeffrey S.  Passel, Ph.D., Urban Institute, Washington, D.C. 

Donald B.  Rubin, Ph.D., Department of Statistics, Harvard
University, Cambridge, Massachusetts

Michael S.  Teitelbaum, Ph.D., Alfred P.  Sloan Foundation, New York,
New York

Karen Woodrow-Lafield, Ph.D., Center for Social and Demographic
Studies, State University of New York at Albany


MAJOR CONTRIBUTORS TO THIS REPORT
========================================================== Appendix IV

PROGRAM EVALUATION AND METHODOLOGY
DIVISION

Robert L.  York, Issue Area Director
Eric M.  Larson, Project Manager
Donald M.  Keller, Adviser
Patrick G.  Grasso, Adviser
Harry Conley, Adviser
Venkareddy Chennareddy, Referencer


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RELATED GAO PRODUCTS

Illegal Aliens:  National Net Cost Estimates Vary Widely
(GAO/HEHS-95-133, July 25, 1995). 

Illegal Aliens:  Assessing Estimates of Financial Burden on
California (GAO/HEHS-95-22, Nov.  28, 1994). 

Tax Administration:  Earned Income Credit--Data on Noncompliance and
Illegal Alien Recipients (GAO/GGD-95-27, Oct.  25, 1994). 

Benefits for Illegal Aliens:  Some Program Costs Increasing, But
Total Costs Unknown (GAO/T-HRD-93-33, Sept.  29, 1993). 

Illegal Aliens:  Despite Data Limitations, Current Methods Provide
Better Population Estimates (GAO/PEMD-93-25, Aug.  5, 1993). 

Immigration Enforcement:  Problems in Controlling the Flow of Illegal
Aliens (GAO/T-GGD-93-18, Mar.  30, 1993). 

Immigration and the Labor Market:  Nonimmigrant Alien Workers in the
United States (GAO/PEMD-92-17, Apr.  28, 1992). 

Immigration:  An Issue Analysis of an Emerging Problem (GAO, Sept. 
1985). 


*** End of document. ***