THIS keeping a lid on stocks: Billionaire Ron Baron

The stock market is closely aligned with the economy, and both are doing fine, but stocks overall are priced about "average" on a historical basis, billionaire buy-and-hold investor Ron Baron said Wednesday.

"People are afraid. They're still afraid, otherwise stocks would be higher," said Baron. He said investors should not be worried because interest rates are historically low; the decline in oil prices is stimulative to the economy; and the deficit is coming down somewhat.

Despite little sign of price pressures, he thinks "there's 4 percent inflation ... [because] everything you look at costs more than a year ago and the year before that and the year before that."

Read MoreWall St sees rate hike in 3Q: Survey

The Baron Capital chairman and CEO told CNBC's "Squawk Box" he would probably have hiked rates for the first time in nine years already, but "our country is too leveraged."

The Federal Reserve is set to conclude its two-day June meeting Wednesday afternoon with a policy statement and a news conference from Chair Janet Yellen. Economists don't expect a hike this time around—widely looking for liftoff in September.

"If people thought [interest rates] would remain as low as they are, the stock market wouldn't be 17 times earnings, it would be 25 or 30 times earnings. So the market has priced in already that interest rates are going to go higher," said Baron.

"They're not going to go higher real fast, because if they did they couldn't service our [national] debt," he said.

Making his case for the relationship between stocks and the economy, Baron said the Dow Jones industrial average, which closed Tuesday at 17,904, nearly matches the $18 trillion U.S. economy.

"You go back to 2007, [gross domestic product] was $14 trillion and it was 14,000 on the Dow. And you go back to 1960, the Dow was 600 and the GDP was $520 [billion]," he added.

Baron formed the investment company that bears his name in 1982 when the Dow was around 880.

With $27.5 billion in assets under management, Baron Capital manages 13 mutual funds with investments in about 450 companies.

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