Commerce Secretary Malcolm Baldrige predicts a far stronger economic recovery than the Reagan administration did at the end of last year because of prospects for a sharp drop in world oil prices.

An unanticipated heavy reduction of inventories and higher sales in the fourth quarter of 1982 also are strengthening the recovery from an 18-month-long recession that was the worst since the Great Depression, the Commerce secretary said in an interview yesterday.

"There's no way I can see that the first quarter is not going to be higher than projected," Baldrige said.

"Because of the good start" for 1983, he said that the nation's unemployment--expected to hover stubbornly around the 10 percent mark--could drop to "the 9 percent area" by the end of the year.

Lower oil prices will help America's transportation industries--especially the airlines and automakers--and such energy-intensive businesses as steel. Steel production, which fell to as low as 38 percent of capacity last year, already has begun rising. It reached 43.2 percent of capacity last month, but that is still below the January 1982 production rate.

Looking at key industries, Baldridge predicted:

* Steel production will increase between 20 and 25 percent over last year.

* Housing starts will go up by 40 percent.

* Automobile sales will jump 20 percent.

But he said these industries are starting from such a low base that their production still will be lower than normal.

Although Baldrige placed no figure on how much better the economy would do during the first three months of 1983, the Commerce Department's chief economist, Undersecretary Robert Dederick, forecast a 4 percent annual rate of growth for the quarter. He also predicted a growth of between 4 percent and 5 percent from the last three months of 1982 to the first three of 1983.

Administration budget estimates included a 1 percent first-quarter growth rate and an increase of 3.1 percent over the last quarter of 1982, when the economy declined by 1.9 percent.

The estimates were made by administration economists early last fall before the signs of recovery intensified. They called for growth rates of 3 percent in the second quarter and 4 percent for each of the last two quarters. Baldrige called these estimates "conservative."

He said that the most significant factor in the first-quarter growth was "the biggest inventory drawdown in the history of the United States by far"--$18.8 billion in the final months of last year--coupled with a 4.1 percent growth in real sales.

These developments had not been predicted inside or outside of the administration, and they set the stage for greater economic growth, he said.

Since then, January figures on durable goods orders increased 9.1 percent, he continued. "That means people are starting to buy something besides houses."

Because of lower interest rates, housing starts jumped 36 percent in January over December and 95 percent over the previous year, and auto sales have been "trending upward" since June on a quarter-to-quarter basis. He called the mid-February decline in auto sales "temporary." Yesterday, the three leading U.S. auto manufacturers released production figures for February that were far above February 1982 levels.

All this happened without the sudden fall in the oil prices of some foreign producers, which have dropped in the past 10 days from $34 a barrel to $30 and which are expected to continue declining.

"If it goes down by $5 a barrel, there's no question it will have a significant effect on gross national product and inflation," Baldrige said.

His personal estimate is that a fall in oil prices alone will add 1 percent to the increase in economic growth and will lower inflation by 1 percent over the next two years. Falling oil prices also will help lower the nation's record merchandise trade deficit, because every dollar that oil prices fall means the United States will pay $2 billion less for the imported oil it buys.