Wednesday's rate increase went a long way toward stabilizing the Federal Reserve's credibility. In the wake of higher rates, stocks rose and pressure in the bond market eased slightly on Thursday morning.

Although the Fed still faces political pressure to lower interest rates, the Federal Open Market Committee voted to raise the fed funds range to 3.75% to 4% on Wednesday. That action, paired with Chairman Kevin Warsh's clear and concise messaging during the press conference, helped restore investors' confidence that the Fed would act decisively when necessary.

"Chair Warsh came across more credible in his communication, delivering a consistent message, aided by a unanimous FOMC vote," writes Andrzej Skiba, head of BlueBay U.S. Fixed Income at RBC Global Asset Management.

The FOMC's policy statement did not mince words, noting that inflation remained elevated and characterizing the rate increase as supporting a "timelier return" to the Fed's 2% inflation goal.

"There was no mention of family fights or task forces; just a very clear and credible statement highlighting that inflation is above target and it will be brought down," writes Felipe Villarroel, portfolio manager at TwentyFour Asset Management.

The credibility stemmed not just from the rate increase itself, but also from Wednesday's summary of economic projections, which showed officials penciling in at least one additional rate increase before the end of the year. Sixteen of the 18 participating FOMC members expect further policy tightening this year. A dozen policymakers penciled in another rate increase this year while four expect two more.

Although markets tend to dislike higher interest rates, Villarroel says the Fed's actions could prove to be good news for the long end of the yield curve.

"If a central bank lacks credibility and investors have doubts about their ability or willingness to address inflation, they will require a higher premium for committing capital for longer periods," Villarroel says. Term premiums should have some respite after the Fed's decision, Villarroel added. But this is not the only factor at play-fiscal policy and high U.S. debt levels remain problematic.

Wednesday's rate increase also showed Warsh following through on what he signaled in his speech during the Jackson Hole Economic Policy Symposium last month.

"We must be confident that underlying inflation is moving to our objective, clearly and at sufficient speed. Otherwise, we have work to do," Warsh said.

His hawkish tone at Jackson Hole sent expectations for a September rate increase soaring, with the Sept. 11 release of the slightly hotter-than-expected consumer price index further strengthening expectations that the Fed would tighten monetary policy. It's worth noting that the Fed has never failed to deliver a policy move that is more than 90% priced in the futures markets in the modern era.

If the FOMC had failed to deliver a rate increase, markets would have reacted harshly. Instead, Warsh's follow-through should go a long way toward restoring investors' faith in the chairman and sharpening their understanding of his reaction function.

"The Fed has largely validated the credibility narrative that had developed since Jackson Hole," writes Daniel Siluk, head of Global Short Duration & Liquidity and portfolio manager at Janus Henderson Investors. Siluk added that Wednesday's decision reduces the risk that investors question the Fed's "inflation-fighting resolve."

But it's too early to tell if Warsh has cemented his credibility. His first two press conferences were largely considered to be missteps and the Fed still has a difficult path ahead to restore price stability in the face of renewed fighting in the Middle East.

The summary of economic projections, however, signaled limited appetite for further increases, with officials projecting just two in total this year-including Wednesday's-and none in 2027.

Raising the fed funds rate by half a percentage point "probably isn't enough to solve the inflation problem," says Oren Klachkin, Nationwide's financial market economist. "Many of today's issues are on the supply side, over which the fed funds rate has little control. What it should do is slow spending on the margin and get us a little closer to the Fed's goal," he added.

In fact, policymakers still expect that it will take more than two years, until 2029, for inflation to return to target, according to the latest committee projections.

Wednesday's actions went a long way toward easing concerns, but with price growth already trending above target for five and a half years, there's still more hurdles for the Fed to overcome before claiming victory on both inflation and credibility.