Federal Reserve Chairman Jerome Powell should be paying close attention to the stock market for clues on whether signs of an economic slowdown warrant a pause in central bank interest rate hikes, economist Ed Lazear told CNBC on Tuesday.

"Given the volatility in the market, and given the fact that [Fed officials] are probably a couple years behind the curve anyway, probably a few weeks worth of patience is not a terrible thing at this point" on rates, said Lazear, who served as chairman of the White House Council of Economic Advisors during George W. Bush's presidency.

For his part, President Donald Trump has certainly made no secret that he wants Powell to stopping increasing rates, repeatedly taking the Fed chief to task publicly and blaming him for hurting the economy and stocks.

The Fed holds its first monetary policy meeting of 2019 at the end of the month. The market expects rates to remain steady at the current range of 2.25 to 2.5 percent. After the Fed's fourth rate increase of 2018 in December, central bankers projected two hikes this year.

However, on Jan. 4, Powell said Fed policymakers "will be patient" on rates given continued muted inflation. Wall Street quickly rallied after its late-2018 plunge. However, the Dow Jones Industrial Average, , and Nasdaq remained in a correction as of Monday's close. Corrections are defined as a decline of 10 percent or more from recent highs.

"The S&P 500 over the past three months or six months, that's the best forecaster of future growth," Lazear said in a "Squawk Box" interview. "The market is forward looking. Most of the other data ... are backward looking."

Lazear, a professor at Stanford University's Graduate School of Business and senior fellow at the Hoover Institution think-tank, was echoing a case he made last week in a Wall Street Journal commentary. "A data-dependent Fed should remain humble about the accuracy of its forecasts, and pay close attention to the market," he wrote.

"If you look at equities, that's a better forecaster than the credit market, credit spread, or yield curve, with one expectation — that short-term rates have a very strong predictive power. But again, that's a direct effect of monetary policy," Lazear said Tuesday on CNBC. "That's because the stock market incorporates the credit market."