Was last week’s 0.4% increase in the consumer price index (CPI) for August enough to convince a wary Federal Reserve that inflation is finally on track to hit 2%?

I doubt it. The big contributors to the increase in the CPI last month were gasoline (+6.3%), a knee-jerk reaction to expected damage to Gulf Coast refineries from Hurricane Harvey; and shelter (+0.5%), which accounts for one-third of the index and increased at its fastest pace in 12 years.

Some economists were reassured by the 0.2% increase in the core CPI after five consecutive monthly increases of 0.1% or less. The August increase raised the 3-month annualized change to 1.9% compared with 0% in May.

For a Fed that has spent the better part of five years wishing, hoping, for inflation to rise — and stands ready with a list of excuses to explain the chronic undershoot — policy makers will need more than one month to convince themselves that the end, 2% inflation, is in sight. (The Fed’s preferred inflation measure is the personal consumption expenditures price index, not the CPI.)

Policy makers have been grasping at straws, some of which are quite thin, to explain the disconnect between the tight labor market and low inflation. Maybe they should start with their flawed model.

Almost every discussion on this subject begins with a statement of fact that the tight labor market, as evidenced by the 4.4% unemployment rate, should be lifting wages and prices.

Note the order: wages and prices. A tight labor market leads to higher wages, which lead to higher prices. This is one of those myths that never dies: cost-push inflation. Milton Friedman was adamant that both prices and costs rise in response to an increase in aggregate demand, which is a function of the Fed’s money creation. Wage and price increases are a reflection of inflation, not a cause of it.

As to the relationship between prices and wages, they generally move together. But prices lead wages, not the other way around. You can read about the relationship in academic literature, or you can think about how businesses operate.

Let’s start with a small-business owner whose company produces widgets. He begins to see a pickup in sales. Pretty soon, his products are flying off the shelf, and he can’t accommodate the increased demand.

What does he do? A rational businessman raises his prices to allocate the limited supply. If he still can’t satisfy the demand for widgets, he may try to increase output using his existing staff, paying overtime if necessary. If he still can’t meet his customers’ demand for widgets at the higher price, he will most likely look to add staff.

In the mythical cost-push-inflation world, a businessman responds to increased demand by paying a higher wage to attract additional workers — and then tries to raise prices to preserve his profit margins.

Which of those examples describes how businesses operate? Good. Let’s move on.

Take a look at the evidence. The 1970s witnessed a high level of unemployment and inflation. The Great Moderation that began in the 1980s saw a peaceful coexistence between declining rates of inflation and unemployment.

Economists have spent a lot of time trying to rationalize low unemployment and low inflation. Some of the hypotheses make sense. For example, global competition and the substitution of robots for humans can exert downward pressure on prices and wages.

Other explanations are getting long in the tooth. The Fed has relied on “transitory” declines in crude oil prices to explain low inflation — ever since crude began its sharp descent in June 2014!

Still others are flimsy. One of the more recent excuses for modest wage increases is that highly paid retiring baby boomers are being replaced by lower-skilled workers, who earn a lower wage.

But lower-skilled workers are less productive by definition, so unit labor costs won’t change.

My favorite excuse by far is that inflation expectations are too low. For the past three years, with brief exception, 10-year inflation expectations have remained below 2%.

I realize I am challenging the entire economic establishment, wedded as it is to the idea that low and stable inflation expectations are the means to ensure low and stable inflation. But this line of thinking implies that the public’s belief can counteract hyper-inflationary monetary policy, such as that witnessed in Weimar Germany in 1923 or in Zimbabwe in the first decade of the 21st century.

“There is something fundamentally wrong if the Fed believes its policies won’t work if people don’t believe they will work,” says a former Federal Reserve economist. “I used to refer to this as ‘Tinker Bell economics.’ ”

Remember “Peter Pan”? Tinker Bell, the fairy, is dying. The audience is told to clap if they believe in fairies.

After the release of the August CPI report, financial markets raised the odds of a December rate hike to about 58%. December is a long way off, especially with Hurricane Harvey denting August retail sales and industrial production, and Irma’s devastation still unaccounted for. For the Fed, “uncertainty” is generally a good reason to stand pat.

What the Fed will do this week, if only because its designated time frame — “this year,” “relatively soon” — is set to expire, is to announce the first step in normalizing its portfolio of $4.5 trillion of Treasury and mortgage-backed securities by allowing $10 billion of securities to roll off each month.

More interesting to financial markets will be any evolution in the Fed’s dot plot. As of June, policy makers were projecting one additional rate increase in December, as well as three more in both 2018 and 2019. Clap if you believe in fairies.

Caroline Baum writes about economics and the Federal Reserve for MarketWatch. Follow her on Twitter.