The regulation of Interest rates has historically been used to control inflation. Higher interest rates dampen demand. At present, inflation is not caused by excessive demand. Inflation is caused by shortages of supply. The global pandemic and Ukrainian war have caused supply disruptions. There are now shortages in materials and labor. How will raising interest rates increase the supply of materials and labor to fix the problem? If the Fed aims is to dampen demand down to match the level of current shortages then that will cause a recession. Is that a smart thing to do?
Without a doubt, demand has outpaced supply over the past 18 months. In labor markets, there are currently 4.9 million more jobs available than there are individuals looking for work (i.e., comparing job openings from the JOLTS release to the number of unemployed workers in the Employment Situation Report), resulting in wage growth that is higher than a level consistent with 2% price inflation. The questioner points out a similar dynamic in product markets: empty shelves and fast-rising prices are evidence of demand outpacing supply. While determining the contributions of demand versus supply is challenging, the simple observation that (real) personal spending is actually above the level predicted by pre-Covid trends (i.e., households are consuming more, not less) suggests that elevated demand is playing an important role.
That said, could the Fed's rate increases that are aimed at slowing demand be counterproductive? Could they restrict supply more than demand and thus widen the gap between the two?
The housing sector may be a useful example to consider because housing is one of the most interest-sensitive sectors of the economy. Higher (mortgage) interest rates clearly tamp down on housing demand. At the same time, the supply of houses may also be restricted by higher interest rates as builders' costs of financing new construction would be pushed up by higher rates. Has housing demand or supply been affected more in the U.S. over the past several months? The clear answer is that housing demand has declined more. We can see this by looking at home prices, as measured by the Case-Shiller National Home Price Index, which peaked in June and have been declining since.
Of course, while housing is an important sector of the economy, it is just one sector. Perhaps dynamics are playing out (or will play out) differently in other sectors. But, the experience in the U.S. (and other countries) over several decades has been that increasing the policy rate leads to tighter financial conditions, followed by weakening economic activity, and then eventually lower inflation.