There appears to be some confusion about the price level and what information it conveys. Some maintain that the price level is irrelevant since it does not reflect changes in relative scarcity. Others, including me, maintain that changes in the price level might indicate changes in relative scarcity. I suspect that the confusion in the first position involves mistaking the price level in our models for the price level we observe in the real world.
The price level in a standard general-equilibrium model is merely a numeraire. It is an index value — a scalar. The magnitude of the numeraire is irrelevant. The only thing that matters is the array of relative prices: the price of apples relative to tomatoes, bananas, automobiles, etc.; the price of tomatoes relative to bananas, automobiles, etc.; and so on. Any price level will enable relative prices to reflect relative scarcity. Hence, a change in the price level — that is, this theoretical price level — is unnecessary.
It is easy to forget that our theoretical price level reflects the weighted average of all prices. Perhaps more tellingly, it is easy to forget how vast the set of all goods being priced in the model actually is. The set of all goods includes every good in every possible state of the world at every point in time. The set includes a bottle of Coke today. It also includes a bottle of Coke next Tuesday provided that it rains before 11:00 a.m. All goods means all goods.
Obviously, this theoretical price level differs significantly from the empirical price levels we construct in the real world. We do not observe the prices of all goods, so we could not possibly construct an index of all prices. The GDP deflator, for example, does not reflect the average price of all goods. It merely reflects the average price of those final goods and services produced domestically in the relevant period. Hence, a change in the empirical price level can indicate a change in relative scarcity.
To see this more clearly, consider a real shock in a simple economy. Suppose we only produce apples and bananas. Typically, we produce 100 apples and 100 bananas. However, following a negative real shock, we only produce 50 apples and 100 bananas. The theoretical price level is unaffected. Since we have fewer apples in the current period, the relative price of current-period apples should increase to reflect relative scarcity. However, current-period apples are also more scarce relative to previous-period apples. Indeed, since apples are more scarce and bananas are unchanged, goods in general are more scarce in the current period. If prices are to accurately convey relative scarcity, the empirical price level will need to increase. Hence, changes in the empirical price level might reflect a change in relative scarcity over time.
This might seem like a pedantic discussion. But the distinction between theoretical and empirical price levels is useful for articulating why one might prefer a nominal-GDP-level target to a price-level target. Ideally, the empirical price levels observed in the real world would vary to reflect changes in relative scarcity over time. When the monetary authority strictly targets a price level, it prevents those changes, thereby undermining the price system’s ability to accurately reflect relative scarcity over time. A nominal-GDP-level target, in contrast, permits the price level to increase or decrease to the extent called for by real shocks. Hence, such a target enables the price system to reflect relative scarcity more accurately than is possible with price-level targeting.