The number of illegal aliens in the United States, according to federal estimates, has dropped by 50 to 75 percent since the mid-1970s - without any massive deportations.
How was this accomplished? Did several million Mexicans and others voluntarily return to their home countries and stay there?
No. The high federal estimates of the mid-1970s that grabbed congressional and public attention and prompted talk of a ''silent invasion'' by illegal aliens, simply proved to be far overstated.
Even now, as Congress considers ways to curb the flow of illegal aliens into the US in the face of high unemployment, the debate over the number of aliens already in the US and the number entering illegally each year continues.
What concerns some US and Mexican analysts is that the discussions on new legislation may, as in the past, prove to be based on inaccurate figures.
In the mid-1970s, when the US Immigration and Naturalization Service (INS) released an estimate that there were up to 12 million illegal aliens in the US, a variety of legislative proposals were offered in response. Then the numbers on which these proposals were based began to crumble.
In the face of critical analyses, the INS lowered its upper estimate to 8 million. In 1980, the US Census Bureau reduced the upper estimate to 6 million. Recently, Robert Warren, a Census Bureau expert on the topic for 10 years, told the Monitor the number of illegal aliens in the US from all nations may be no higher than 3 million and as low as 1.5 million.
Of these, says Warren, some 1 to 2 million are probably Mexicans.
A Mexican scholar here called Mr. Warren's estimates ''very important'' because they represent the first time a US government estimate of Mexicans in the US illegally has come fairly close to a Mexican government estimate.
The Mexican government questioned some 100,000 undocumented workers being returned to Mexico during four months from 1977 to 1979. From this came their preliminary estimates that some 500,000 to 1.2 million Mexicans are in the US illegally at any one time, more in summer than winter. (A US Census Bureau team, not including Mr. Warren, thinks the Mexican estimate is somewhat low.)
In a second finding, based on interviews with some 62,000 scientifically selected families in the winter of 1978-79, the Mexican government estimated that nearly 1 million Mexicans 15 years of age or older were in the US during at least part of 1978 working or looking for work -- most of them without legal entry documents.
What these surveys could not measure was the number of Mexicans living illegally in the US on a permanent basis. One Mexican Department of Labor analyst speculates there may be 250,000, to 350,000.
The old INS figures were ''based on politics, not research'' charges Jorge Bustamante, a sociologist at the Colegio de Mexico and a leading expert on undocumented Mexican workers.
Mr. Warren, who has examined internal INS communications regarding the earlier high estimates of illegal aliens, says he found no sound methodology for them. An INS statistician, in a Monitor interview, concurred.
''Those numbers have never -- and still don't have -- any basis at all,'' Warren told the Monitor. ''They were used for various purposes.'' One purpose, he suggests, was to win a larger appropriation from Congress for the INS.
The overstated figures did focus public attention on the issue, but they also caused unnecessary fears about the numbers involved, says Warren.
The old INS estimate of 12 million illegals is still being used, however, by some in calling for legislation to curb illegal entries. Rudolph Oswald, research director of the AFL-CIO, cited the figure recently in a Monitor interview. But when asked if he had any way to justify the now widely discredited figure, he said he did not.
But Warren's estimates of 1.5 to 3 million illegal aliens in the US are preliminary ones. In presenting its immigration legislation proposals to Congress last year, Reagan administration officials relied on the 1980 study by a Census Bureau team.
Yet in referring to that study in congressional testimony last fall, Acting INS Commissioner Doris M. Meissner said the study estimated 3.5 to 6 million illegals in the US. Attorney General William French Smith, in testimony before the House and Senate subcommittees on immigration last summer, called these figures ''basic facts.''
In fact, the Census Bureau study does not say there are 3.5 to 6 million illegals in the US. The study, examined by the Monitor, says the total ''is almost certainly below 6 million . . . possibly only 3.5 to 5 million.''
And far from calling their estimates ''basic facts,'' the authors of the study conclude:
''We have unfortunately been unable to arrive at definitive estimates of the number of illegal residents in the US or of the magnitude of the migration flow. Therefore, policy options dependent on the size of this group must be evaluated in terms which recognize this uncertainty.''
Given the difficulties of enumerating them, estimating the number of illegal aliens in the US is ''a guessing game,'' says Wayne Cornelius, director of the US-Mexican studies program at the University of California at San Diego.