Short answer: In a word, NO.
Long answer: It's a very nuanced and complicated issue, but in practice, hiking interest rates generally does more harm than good, and at best is really not very effective in fighting inflation.
Interest rate hikes, far from being a "razor-sharp, double-edged sword" (as we at the TSAP used to say) in theory, they are in practice just as blunt of an instrument as tax hikes are. And they only "work" insofar as they cause a recession, as history has shown. When the FERAL Reserve raises interest rates, it is "pushing on a a string" when they raise them insufficiently to cause a recession, and "blunt force trauma" to the economy when they raise them enough to do so. And when they cut rates, it is even more so like "pushing on a string", as the damage is usually already done by that point, and of course they cannot cross the "zero lower-bound" into negative rates without inherently turning the world of finance upside-down. There seems to be no "Goldilocks zone" for interest rate policy during times of high inflation, and the "therapeutic window" is generally closed.
Knowledge says that choking the economy until it goes limp and then choking it some more technically reduces inflation by killing demand for goods and services. But wisdom says that one could hardly call that a success.
Not only are interest rate hikes inherently recessionary, they can also paradoxically increase one of the two types of inflation, "cost-push inflation", even as they tamp down the other type, "demand-pull inflation." Both types are two sides of the same coin, so it can easily result in (or exacerbate) chronic stagflation, for which the only "cure" is to hike the rates so extremely high to cause a deep recession or depression, followed by cutting rates very quickly, at the cost of massive collateral damage. A "cure" that is worse than the disease.
And the fallout falls not on the rich, who are largely insulated from the consequences, but overwhelmingly on the poor and working class, and also the middle class as well.
Cutting the money supply, whether fiscally via austerity or monetarily via quantitative tightening, is also similarly recessionary and damaging as well. Both forms of tightening, along with interest rate hikes, are at best "break glass in case of emergency" measures that should almost never be used, period.
In other words, if you "burn the village to save it", the village will eventually return the favor. You reap what you sow. That's literally how karma works.
Even Rodger Malcolm Mitchell himself has recently turned against the idea of interest rate hikes, a policy he once strongly supported. That really says something indeed. Ellen Brown would agree as well.
So what works instead? According to Mitchell, the root cause of ALL inflations is shortages. Whether it's oil, gas, energy in general, food, labor, or otherwise, shortages are the common denominator. To cure inflation, we must cure the shortages. Now that is often a lot easier said than done, but governments who issue their own currency can help resolve shortages by fiscally incentivizing more production of such scarce goods and services. And, of course, to also refrain from creating shortages in the first place with things like price controls or other artificial restrictions by fiat that are known to backfire.
Oil, gas, or energy shortage? Incentivize more domestic oil/gas production in the short term, followed by renewable energy production in the medium to long term as well. Buy oil/gas or energy at at premium and resell it or give it away at a loss. Food shortage? Buy food at a premium and resell it or give it away at a loss. Computer chip shortage? Incentivize domestic chip factories. Labor shortage? Implement a "reverse payroll tax" like the EITC but simpler and more straightforward, to boost the paychecks of workers without increasing costs for employers. Or the government can hire the most in-demand workers directly at a premium. And consider replacing all or some means-tested social welfare programs with an unconditional Universal Basic Income (UBI) that does not perversely penalize people for working. And so on. That's the power of creating one's own currency via Monetary Sovereignty.
QED. Case closed, at least until we find even more compelling evidence otherwise. Therefore, the TSAP's new position in interest rates shall supersede everything we have said in the past about the topic.
UPDATE: So what is the ideal interest rate then? Should we do what MMT advocates, and just park it at zero and leave it there? There is a good case to be made for that, and the answer probably depends on a number of factors. But negative interest rates are really not a wise idea for a national currency (too negative and people just hoard cash under the mattress, while not negative enough is really no better than zero). For complementary and alternative local currencies, negative interest (aka demurrage) can perhaps make sense, like the Austrian town of Worgl famously did during the Great Depression, but the benefits of such likely do not scale up very well. Thus for national currencies, zero is the practical lower bound. And if zero interest (i.e. being able to borrow money for free) is still not stimulative enough, then do "QE for the People" by printing more money and giving it directly to everyone, rather than the banks in "regular" QE. Problem solved.
James Gailbraith makes a great case for low interest rates overall.
Thus, like MMT, the natural interest rate should be assumed to be zero by default, but unlike MMT, we should still not tie our hands and take higher rates off the table completely as a "break glass in case of emergency" measure. Nor should Treasury bond sales be completely discontinued either, as those help stabilize the financial system in times of instability.
But what about speculative bubbles? Don't low interest rates encourage those? Yes to some extent, but only if Wall Street is deregulated like the Wild West (like now). Therefore, better regulation of the big banks and shadow banking system, and a financial transactions tax, are a better idea to rein in reckless speculation than high interest rates.
TL;DR version: In a nutshell, raising interest rates has a tendency to backfire and generally does more harm than good, once all the jargon and accoutrements are stripped away. Occam's Razor would say that deliberately making everything effectively more expensive across the board (by making money itself harder and costlier to get) to engineer a recession is a terrible way to fight inflation, and can only encourage a perpetual quagmire of stagflation.
What about the Canadian experience in the 1980s? Well, their inflation and unemployment were even worse than the USA despite (or more likely because) they kept their interest rates higher for longer. And that disparity persisted well into the 1990s, until they devalued their overvalued currency, and then cut interest rates, which seemed to solve the problem.