17 try to factor amnestied immigrants into the illegal immigration component, according to their initial status upon arrival in the United States.

Illegal/Undocumented Immigration. Illegal immigration is the most difficult component af international migration to estimate reliably. Estimates of illegal immigration rely on a number of different methods, including the following: direct counts through sample surveys, censuses and surveys in countries of origin, the Delphi method, apprehension statistics, matching studies, migration histories, comparisons of different data sources, analysis of vital statistics, and airline traffic statistics. Estimates of the stock of undocumented immigrants in the United States vary widely and estimates of the net annual flow are even more difficult to come by. Nevertheless, it appears that permanent illegal immigration in the 1980s has been much smaller than has often been suggested (Bean and de la Garza, 1986).

Some analysts have suggested that as many as 500,000 illegal immigrants are added to the U.S. population every year, but there is no evidence to support this conclusion. Many of these estimates are based on the large number of undocumented immigrants apprehended each year by the Immigration and Naturalization Service. Since 1977, an average of more than one million apprehensions have been made annually with the largest number (1,767,400) being apprehended in FY1986 (Immigration and Naturalization Service, 1988a: Table 59). However, apprehension statistics cannot give any more than a crude indication of the level of permanent illegal immigration for several reasons. First, return migration among undocumented immigrants who do elude detection is very substantial. In recent years, more evidence has become available on the circular nature of undocumented immigration. Second, it is not clear whether an increase in apprehensions suggests an increase in those who get through or a decrease because of more effective enforcement. Finally, there is substantial double-counting in the illegal immigration accounting system since the same individual may be apprehended many times. In fact, the "revolving door" operates so efficiently that at least one individual was apprehended and returned to Mexico five times in the same day.

Estimates of the stock of illegal immigrants at various points in time do not support the existence of very large-scale net flows of illegal immigrants in recent years. A 1978 review of immigration studies by the Select Committee on Population of the U.S. House of Representatives concluded that most objective experts pegged the stock of illegal immigrants at 3-6 million at that time (Select Committee on Population, 1978). A similar review by the Committee on Population and Demography of the National Academy of Sciences in 1985 concluded that the stock of illegal immigrants was probably lower than the 3-6 million estimated seven years earlier. As part of the NAS study, Hill (1985) concluded that a stock of 1.5 to 3.5 million illegal aliens in 1980 is reasonably consistent with most studies. Moreover, he found no empirical basis for the belief that the illegal immigrant population increased sharply in the early 1980s.

In assessing the effect of illegal immigration on net international migration to the United States, it is important to note that many illegal immigrants eventually obtain green cards and become legal residents (Houstoun, 1983). Therefore, we have to be careful not to double count these immigrants