Path targeting or level targeting is a policy proposal which says that if, e.g., you are a central bank whose sole nominal target is the price of widgets, you should not say:

"Each year, we want the increase in widget prices to be around 2%."

Instead you should say:

"We want the price of widgets to be $1 in year 1, $1.02 in year 2, $1.04 in year 3, and so on."

Then even if you undershoot the target in year 2 and get a price level of $1.01 instead of $1.02, you don't change the targeted level of $1.04 in year 3. You just create additional money in year 3 to hit the same price target as before (aka, you try for 3% inflation to "make up" for the previous undershoot).

On a path target or level target, a central bank's error in one year has no effect on expected prices in future years: everyone still expects the bank to target $1.04 next year, then $1.06. Even if the central bank is consistently undershooting its target by $0.01 every year, on a level target this merely means the actual path for year 2 and on is $1.01, $1.03, $1.05.

Conversely, targeting "2%/year inflation", without targeting a stable future path, means that if you undershoot and only get $1.01 in year 2, you will now say you want a $1.03 price level in year 3. This means that when you create too little money in year 2, you've now also said you want to create less money in the future, which adds an additional deflationary force. This is a form of destabilizing feedback.

We could evaluate the wisdom of path targeting for e.g. inflation (though a better target might be NGDP) by asking the key question of whether measured inflation of 2%, 2%, 1%, 2%, 2% is experienced by the economy as being more destructively volatile than 2%, 2%, 1%, 3%, 2%. E.g., consider these two channels of damage:

"Oh, no! I didn't expect money to be worth that much in year 5! I can't afford to pay off the nominal loans I took out in year 1!"
"Oh, no! My computer automatically prints menus where the numbers go up by 2% from whatever they were in the previous year, and now I have to reprint my menus!"

We'd like to have a less straw example above, and solicit suggestions. In our defense, we're finding it hard to come up with a case where the causal impact is clearly being mediated by the this-year-vs-last-year ratio, and not by the ratio for this-year-vs-2-years-ago.

Path targeting is particularly advocated by market monetarism, an NGDP-centric view which suggests that stable long-term growth in NGDP and predictable levels of future NGDP are economic factors of far greater importance than the isolated ratios for this-year-vs-last-year.

The prominence of path targeting in market monetarism also reflects concern by market monetarists that in sluggish modern economies (e.g. Japan, the European Union, arguably the USA), the actual sequence of inflation numbers often tends to look like 1.3%, 1.5%, 0.5%, 0.3%, 1.5%. In other words, where the central bank is turning out to be not very good at hitting its targets and is repeatedly missing in the same direction, a path target should be much more predictable and much less volatile than targeting the this-year-vs-last-year ratios as isolated numbers.