I like a good rally, but the market overreacted—we are hardly near achieving the Fed’s 2% inflation goal.

In April, the Consumer Price Index was up from March at a 3.8% annualized rate. That’s below the 4.6% in the first quarter but above the average for the prior 12 months—3.4%.

Simply, for the last year, monthly changes in prices have bounced around and the progress recorded for May could just as easily be worse or better.

Stripping out food and energy, core prices were up 3.6% from March to April—the same as the 12-month average for month-to-month changes.

The history of struggles with inflation indicates the Fed should not lower interest rates until inflation hits the 2% target, and policymakers are confident that level is sustainable. Easing back too soon would likely result in inflation reigniting and the Fed having to raise rates again.

Housing services account for 36% of the CPI, and policymakers have anticipated that a declining pace of increase for apartment rents, as recorded by industry surveys, would bring down housing inflation.

However, the lion’s share of the shelter component in the CPI is the imputed rent on owner occupied homes—what homeowners anticipate they could obtain renting their properties.

Since the Global Financial Crisis, the pace of new home construction has slowed. Over the last year, even with higher mortgage rates, resale prices on single family units rose more than 7%.

The shelter portion of the CPI is up 5.5% over the last year and will not likely rescue us from inflation.

Services, other than housing, account for 25% of the CPI and were up 5.1%. These are labor intensive, and prices are considerably sensitive to wages.

The labor market may no longer be red hot, but we still have about 30% more job openings than unemployed workers.

All along, Fed policy has not been as tight as the task requires.

Inflation reached 8.5% in March 2022. And the Fed ultimately raised the federal funds rate—the overnight rate that banks charge each other to borrow reserves—to 5.3%, or about 62% of peak inflation

When Paul Volcker slugged it out with inflation that peaked at 14.6 percent in 1980, he pushed the target interest rate all the way to 19.1%.

Complicating matters, President Joe Biden’s fiscal policies have an inflationary bias.

The Congressional Budget Office estimates the federal deficit will be 5.6% this year and 6.1% in 2025. Up from 4.6% just prior to the pandemic, the International Monetary Fund estimates those larger deficits add about half a percentage point to inflation.

Mr. Biden’s Climate Change agenda has similar consequences.

The cost of installing a new air conditioner is up thousands of dollars. Overall, complying with new energy conservation and emissions standards is raising new home prices an estimated $31,000.

The recent surge of immigration, enabled by Mr. Biden rolling back many of President Donald Trump’s policies, allowed employment growth of about 250,000 a month in 2023. The sustainable pace under the prior immigration regime would been about 100,000.

All those additional workers are out looking for apartments—no surprise, the vacancy rate in New York City is at an historically low 1.4%.

Moreover, the recently approved $95 billion aid package for the Ukraine, Israel and Taiwan, and Mr. Biden’s program to forgive an additional $475 billion in student debt will add to the federal deficit.

Now a bipartisan group of senators is proposing the Pentagon spend an additional $32 billion annually on Artificial Intelligence to keep pace with Chinese and Russian military capabilities.

At the end of 2025, most of the personal tax provisions of the 2017 Tax Cut and Jobs Act will expire. Few observers expect these will be permitted to lapse entirely, and extending those without raising other taxes could cost up to $4.8 trillion over 10 years.

It’s safe to assume that the stimulus to aggregate demand and inflation created by bigger deficits will grow.

Ordinary folks see this in their lives—groceries are taking the largest share of family incomes in three decades, and low wage workers struggle with food insecurity.

Consumer expectations for inflation over the next year, as tracked by the Conference Board, University of Michigan and New York Federal Reserve average about 4%.

In an environment like this, the Fed should not be talking about easing monetary policy. Rather, it should recognize that interest rates may yet have to go higher.

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Peter Morici is an economist and emeritus business professor at the University of Maryland, and a national columnist.