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Does it mean Fed's policy makes the US economy slow down? https://www.collinsdictionary.com/dictionary/english/lag
In an interview with Reuters on Wednesday, Cleveland Fed President Loretta Mester said, "I'm not one who would like to see inflation be at 2 percent before we continue on the path" of rate hikes because policy affects the economy with a lag.
Source: http://www.reuters.com/article/us-usa-Fed-minutes-idUSKCN1AW2AW
With a lag here means "not immediately, but after some time".
Ms. Mester says that the Fed should continue raising interest rates now rather than waiting for inflation to increase; she expects inflation to rise in the future, and because it takes some time for the Fed's action ('policy') to have any effect on the economy, she believes that the Fed should take action now so that its effect is in step with rising inflation rather than 'chasing' it after the fact.
Not to disagree with the other (correct) answers but to address the underlying structure and the cause of your confusion...
Consider the following sentences (as this is how you are understanding with a lag):
The bat bite infected him with a virus.
Policy affects the economy with a lag.
There, the virus is something that happens to him. On that model, you are understanding lag to be something that happens to the economy. But there, "with a lag" modifies affects, not economy.
Consider:
After twisting his ankle, he ran the race with a limp.
"with a limp" modifies (or complements) "ran", not "race". He ran with a limp.
Thus:
Policy affects the economy with a lag.
Policy affects with a lag (a delay).
The effects of policy upon the economy are not immediate.
It means "because policy affects the economy slowly". Economic measures takes more time than monetary measures (rate hikes) to affect the economy (have effects on employment, GDP growth etc.)
Adding to Tᴚoɯɐuo's answer. I don't have enough reputation for commenting yet.
The bat bite infected him with a virus.
There, the virus is something that happens to him.
The word "virus" here actually modifies the word "infects". The infection is what happens to him.
Consider these examples:
The bat bite infected him with rabies.
The noun is getting modified by the verb, and the verb is getting modified with the "with _______" phrase. If you think about it this way, you can see that all of the examples actually follow the same pattern:
Policy affects the economy with a lag.
The economy is affected. The effect works with a lag.
After twisting his ankle, he ran the race with a limp.
The race is ran. The running is with a limp.
The bat bite infected him with a virus.
He is infected. The infection is with a virus.
