Government housing specialists split with economists in the private sector this week over the future of mortgage interest rates.

At a symposium entitled "How High is Up?", sponsored by the corporate relocation company Executrans, they differed on whether interest rates have yet hit their peak. The more pessimistic view was put forth by the private sector.

Kenneth M. Plant, vice president for research of the Federal Home Loan Mortgage Corp. (the governmental secondary mortgage market maker known as Freddie Mac), predicted that interest rates would peak in the last part of this year, decline through mid-1979 and then rise modestly in the second half of the year.

That would mean that conventional, 80 percent loan-to-value ratio loans, now at 9.85 percent, would dip to between 9 and 9 1/4 percent before rising to between 9 1/2 to 9.375 percent.

Arnold H. Diamond, director of the office of financial management at the Department of Housing and Urban Development, was slightly less optimistic. He predicted that interest rates would not decline significantly until early in the second quarter of 1979. At that time a slowdown in real economic growth is likely to result in lower rates, he said.

Economists from the private sector, Kenneth Kerin of the National Association of Realtors and Michael Sumichrast of the National Association of Home Builders, said they expect interests rate to hover above 10 1/4 or 10 1/2 percent during the next few years.

Arthur M. Weiner, consulting economist for the U.S. League of Savings Associations, presented the most pessimistic picture, of rates in the 10- to 11-percent range "for most areas for some months."

There was general agreement that mortgage money would be available, although here again the private sector was less optimistic. Plant said it would be plentiful as decreasing interest rates on Tuesday bills and other instruments draw more investors back toward thrift institution. Diamond predicted sustained availability but at a somewhat lower level than the volume produced in 1978.

Weiner said he felt that money would not be as readily available in 1979 as it is now because the cost of money to thrift institutions since the new money market certificates pegged to Treasury bill rates went into effect is advancing more rapidly than mortgage rates.

As for demand, the government's economists again proved somewhat more optimistic. Diamond of HUD predicted that housing starts would reach 1.8 million in 1979. Freddie Mac's Plant pointed at from 1.7 to 1.8 million starts, the second quarter of 1979 being the weakest and the fourth the strongest.