For much of her tenure as head of the Federal Reserve, Janet Yellen has been pressured by Republican lawmakers who want the U.S. central bank to adopt a monetary policy rule, a straightforward formula connecting unemployment and inflation to a benchmark interest rate.

On Saturday a Yellen ally and former adviser at the Fed delivered a provocative retort: the economic models underpinning those simple rules don't work that well, and the best policy decisions come when central bankers look beyond those models to the unexpected forces shaping the economy.

Former Fed Chair Alan Greenspan famously did it in the 1990s when he argued against a rate hike at a time when rising productivity was holding down inflation, and arguably failed to do it when he ignored the impact of the tech and housing bubbles, Johns Hopkins University economics professor Jon Faust said in a paper presented at an annual Fed conference here.

In each case the point is the same: it was the extraordinary events outside of the basic inflation and output models used by central bankers that ultimately mattered most, argued Faust, who served as a special adviser to the Fed's board of governors until September 2014.

That approach "brings fears of 'seat-of-the-pants' policymaking and, for the more excitable, of barbarians at the central bank gates," Faust wrote.

But after reviewing the statistical models that try to separate underlying economic trends from other factors, Faust said he concluded it is those other factors that policymakers often need to understand and reflect in their decisions - something that can't be done through a rule.

"Normal cyclical dynamics ... have played a distinctly minor role in both the successes and failures" of monetary policy, Faust wrote. "Understanding ... confounding dynamics has always been the key to good policymaking and failure to understand those dynamics has played a key role in major policy mistakes."

Sophisticated econometric models of inflation, for example, may include "extra wiggles" in the forecast as inflation moves from its current rate to a long-run average, but on the whole do no better than a "mindless" line drawn between the two points, he said.

His argument has bearing for the push by Republicans in Congress and possibly by the party's eventual 2016 presidential nominee to tie the Fed to a policy rule.

Yellen is arguably facing a "seat-of-the-pants" moment now in judging whether it is time to raise rates, a call tied closely to her judgment about when and how fast inflation might rise to the Fed's 2 percent target.

That's a decision no model or rule will help with, Faust suggested.

"Policymakers must take a stand," he said.

(Reporting by Howard Schneider; Editing by Paul Simao)