Joe Gross is 19, black, tough and has the kind of checkered job history that most company personnel directors don't want to read:

After dropping out of high school in the 10th grade, Gross did some odd jobs for an uncle for a couple of months and then got arrested for car theft. After two years in a detention center, he's back in the labor force.

Education: No high school diploma.

Job experience: None, except for his stint at the detention center.

Marketable skills: None

Perferred location: Must be close to Gross' Dorchester housing project. Although there are few jobs in the neighborhood, Gross is adamant: "If you work too far away," he insists, "you aain't going to be able to survive."

What to do about hard-to-employ youths like Joe Gross has become a major problem for government policy makers in the past few years -- both in the United States and virtually every major industrial nation.

National unemployment figures consistently show shockingly high jobless rates for the 16-to-24-year-old category. The unemployment rate for youths overall here is 19.2 percent -- almost triple the 7.8 percent rate for all workers.

For black youths, the jobless rate is a staggering 35.2 percent. And it has been rising sharply as the recession worsens.

Moreover, although the government has pumped billion of dollars into special youth employment programs over the past several years, policy makers still aren't sure precisely which -- if any solution actually works.

The Carter administration, groping for an election-year initiative, last January proposed a $2 billion youth program designed to link stepped-up education efforts with after-school jobs to prod youngsters to stay in school.

But with the economyy in a recession -- and the program phased in gradually for budgetary reasons -- no one expects the problem to be resolved soon, even if the new Carter effort does prove worthwhile.

At the same time, there are fears that unless some progress is made quickly, the nation will suffer grave consequences through still further-rising crime rates and -- possibly -- increased social unrest.

"There's a feeling that there's a bit of a time bomb ticking away out there," said Isabel V. Sawhill, co-author of a newly published report on youth unemployment with Bernard E. Anderson of the Rockefeller Foundation. y

There are two major aspects to the nation's youth unemployment dilemma:

First, the problem isn't nearly as broad in scope as the statistics would suggest. Second, for the small number who actually are affected, the situation is truly serious -- and defies any easy solution.

In a way, the numbers are deceptive. While it's true that the jobless rate for youths reached an average 16.1 percent in the U.S. last year, most of those were far from what a majority of Americans would be likely to regard as hardship cases.

Relatively few of the nation's youth actually are breadwinners for their families. Most are seeking only part-time jobs. And a large proportion work only for brief periods and then drop out to do something else.

Even among black youths, where the unemployment rate soared to an mind-boggling 33 1/2 percent in 1979, the problem isn't large numerically. The figure represents only 347,000 persons -- out of a teen-age work force of 9.5 million.

Moreover, surveys show that even of that 347,000 at least 110,000 were looking for temporary jobs, not permanent openings. About 135,000 were looking for part-time work. And about three-quarters of these wanted after-school or weekend jobs.

And a recent study by the National Bureau of Economic Research shows that almost half the teen-agers classified as unemployed also are in school -- a plight not nearly as serious in terms of social policy as when an adult is out of work.

For most of these youths, the job outlook depends primarily on the strength of the economy. During recessions, youth jobs are relatively scarce. But during more heady times, there are plenty of slots to go around.

Experts say only a few hundred thousand youths really face serious trouble in getting and keeping jobs over long periods of time.

The difficulty, however, is that for this hard core of really badly off youths -- mostly black and Hispanic -- the situation is truly serious, and so frustratingly complex that it defies any easy solution.

The research bureau's study, for example, estimates that more than half of all teen-age unemployment is concentrated among only 10 percent of all youths.

"However," the study concludes, "the concentration of unemployment among a small fraction of youths has presumably higher social costs than the even distribution of unemployment among all young persons might have."

Those who fail to find jobs soon after leaving school face the likelihood of spotty employment and near-poverty wage levels virtually for the rest of their lives. Many end up on the welfare rolls or in jail.

The difficulty is that while the youth problem has been analyzed over and over in recent years, there's been little real progress in determining either its causes or solutions.

For a long time, economists believed that the bulk of the problem was demographic -- that the population "bulge" created by the war-baby boom simply flooded the job market and made it difficult for teen-agers to get jobs.

The theory here was that the youth unemployment situation needed no major new government programs -- that the youth problem simply would "disappear" once the war-baby bulge passed the 24-year-old mark and entered the work force.

Now, however, the prevailing view is that while the demographic shift may ease the problem overall, the crunch will become more acute for black and Hispanic youths.

"The demographics are making the numbers more manageable, but the problem is still a severe one," said a government economist who has studied the figures closely. And the total of hard-core unemployables is growing." *tCharles McLean, a Boston researcher who has been surveying hundreds of inner-city teen-agers who have been unable to find jobs, says another major factor is the youths' "lack of information about the world of work."

McLean said he was "shocked" during the survey by how little the youngsters knew about how to get and hold jobs -- from the simple ability to answer questions about themselves to understanding what is expected of them on the job.

McLean also points out that most youths from these poor neighborhoods have no one to turn to in the family either for a role model or for help in finding a job, as more fortunate youngsters do in starting out to work. h

What makes youth unemployment so serious a problem is not so much the threat of unrest -- although that has sparked the government action in most previous efforts -- but the impact of such joblessness on a youth's job prospects later.

Studies have shown that although college-bound youths aren't affected much by inability to get jobs during their school years, others who are unemployed during their teens earn lower wages throughout their working years.

Over the past two decades, the government has tried a plethora of new programs to attack the problem -- from highly-trumpeted summer jobs programs to 1930s-style Civilian Conservation Corps camps.

By common agreement, however, most have failed dismally to deal with the problem. The lone exception has been the Job Corps, which sends inner-city youths to special training camps. But it's exceedingly expensive.

Joe Gross, who was a jobless statistic earlier this year, now is on the employment rolls, at least for the forseeable future. Five weeks ago, Gross got a job as a structural steel maker. Wages: $5 an hour for a 35-hour week.

But for many other inner-city youths, the picture looks bleak and threatens to remain so for the next several years. For all the money being spent on the youth unemployment programs, no one yet fully knows how to cope with the problem.