Added to the ever-repeated articles exposing nursing homes, battered children, marijuana smuggling and paving contract scandals, the last few years have given us illegal immigrants. Their number is unknown, but whether there are 3 million or 20, the "problem" is so serious even President Carter has addressed it.

It's easier to invent solutions, however, than to say exactly what the problem is. Since most of the illegal immigrants are Mexicans and other Latin American xenophobes who don't like the thought of having their children play with the children of such exotic people. In which case the only problem is the people who think the immigrants are a problem.

In the past, labor unions have often been against large-scale immigration, be it legal or illegal, but these new arrivals only have a distant and putative effect on native-born Americans' job possibilities. The illegal immigrants take the jobs we natives scorn - farm and marginal factory work as well as domestic services and the clean-up, no-prestige tasks in our hospitals and health care institutions.

Termination of illegal immigration might mean the termination of a number of those jobs. The small shops and factories where many an illegal immigrant works does the kind of subcontracting that can be quickly switched to Haiti or some cooks and cleaning ladies, while other tasks that other low-labor-cost location. A number of higher-income homes would find themselves without can't be dispensed with or relocated to cheaper climes would be automated. In a place like Washington, D.C., for instance, where once practically all waiters were black, they're now either Latin American or European or even native whites. If those who were illegals were forced out of these jobs, the wages would probably rise high enough so that others might decide the money was good enough to reenter- the market.

But for the number of jobs that would be "created" in this fashion for native-born Americans, an unknown, but possibly equal number of jobs might be lost. MIT economist Michael Piore (in the March-April issue of Working Papers) points out that there are a number of declining industries that make it by mixing higher-paid natives with lower-paid illegals on the same payroll.

Stopping the flow of illegals is a mixed blessing that will increase the costs of a number of goods and services that both the native-born wealthy and non-wealthy now get comparative bargains. Yet those bargain wages look very good to the men and women who slip into the country from afar. In that connection, incidentally, it is not a proven fact that American employers violate the law by paying illegals less than the minimum wage. There are instances of that, as well as dangerous and unhealthy working conditions in the shop, but apparently many employers save enough by omitting non-mandatory fringe benefits not to have to break the law.

Piore says that, consciously or unconsciously, the Immigration and Naturalization Service, which is supposed to keep illegals out of the country, enforces the laws so as to prevent competition with our native workers. Thus enforcement is heaviest in the Southwest where there are many Mexican-Americans who are citizens and who might otherwise have to compete with the illegals. They are chased into California and the Midwest where there is a larger unmet demand for low-wage, low-status labor.

In like manner, Piore reports that the Service starts raiding restaurants and hotels when school lets out in the spring. That clears out the illegals and lets native-born high schoolers have jobs for their summer vacations. In the autumn, the illegals are alowed to drift back in. Apparently the same enforcement practices follow the rhythms of the business cycle. Piore notes that when the construction industry went plop in 1974-75, the Service chased Canadian building trade workers out, though it had previously winked at them when there was a shortage of skilled labor.

Looking ahead, some analysts are predicting that in a few years we may be happy to have our Latin American visitors. With the shift in our native birth rates, we are already on the verge of having an aging work force. For awhile that will be pleasant because it's going to take care of our concern over teen-age unemployment, but after that it won't be so enjoyable.

We may come to regret we weren't as hospitable as we might have been. We may also regretthat we didn't do more to educate and train the children of today's illegal immigrants, when, in another 10 or 15 years, we discover there are no warm bodies to fill in the higher status, pay and skill jobs.