Billionaire hedge fund manager Bill Ackman said Tuesday that the U.S. economy is not in a recession right now but that the Federal Reserve needs to be significantly more aggressive to defeat inflation. The CEO of Pershing Square Capital Management told CNBC's " Squawk Box " said that Federal Reserve has so far failed to tighten monetary policy enough to hold down inflation. "The biggest problem for the economy right now is inflation. Inflation is roaring, it's continued to rage, and unfortunately the steps taken by the Federal Reserve have not been effective," Ackman said. Last week, the Federal Reserve hiked its benchmark interest rate by three-quarters of a percentage point . That brought the Fed Funds rate to a target range of 2.25%-2.50%. Ackman said the Fed needs to be aggressive and push its rate to near 4% or above, saying that the economy was entering a period of "persistently higher rates." "I think rates are going to need to stay 4%-plus for the foreseeable future — 12 to 18 months, or so — in order to kill this inflation. And they may need to take rates higher," Ackman said. "The biggest risk to the markets is that people are not pricing that in." The hedge fund manager also warned that "the wage-inflation spiral is underway," a phenomenon that economists believe can make inflation more permanent. Pershing has interest rate hedges in place that would benefit from short-term rates and the 30-year Treasury yield moving higher, Ackman said. Ackman said he does believe the economy is "very strong" right now and said he was pleased with the performance at some of his Pershing's portfolio companies, including Lowe's and Chipotle . He also cited a recent conversation he had with JPMorgan CEO Jamie Dimon that made him optimistic about the economy even as inflation starts to hurt consumers. "Jamie talked about, number 1, this is the lowest default rate period in history for the consumer part of the bank. Their full spectrum of people, poor to rich, that bank with JPMorgan and Chase and so on, are in the best position they've ever been," Ackman said.