Nominal GDP IS nothing more than the product of prices and output. To say that a fall in nominal GDP relative to trend "caused" the fall in the path of prices and output relative to trend is just gibberish.
In terms of the calculation of the statistics, it is more accurate to say that real GDP is nothing more than nominal GDP divided by a price index..
Nominal GDP is calculated by adding up price times quantity for a variety of goods and services. The prices and quantities are thing that are observed. The product of each one is something that actually happened, the amount spent on each product by buyers and the amount earned as revenue by sellers. And the sum is something that is true of the economy.
The price level is measured by calculating an index. The index compares some weighted average of the prices to those in a base year. While the prices today and those in the base year are actually measured, the weighting in the years and adjustments for the fact that the goods are somewhat different makes the price index much more than something actually observed. The price index is not something that happens in the economy.
And then when this created price index is divided into the nominal GDP, we have something that isn't really the volume of goods produced. It is what the dollar value of the goods produced would have been if prices were what they were in the base year, leaving aside weighting issues and adjustments for quality.
If we model the macroeconomy with a single good, and imagine that the output of that good is given entirely by real factors, then real GDP is simple. Say a billion bushels of corn are grown in an economy that solely grows corn. Real GDP is a billion bushels of corn.
Of course, there are no relative prices in this economy. The price level is simple. It is just the money price of corn. And so, nominal GDP is the simply the quantity of corn multiplied by the price of corn.
Nominal GPD still tells us something about the economy. It is how much money is spent on corn and how much money is earned by selling corn. But still, it is entirely plausible to imagine that the price and quantity are first set and that nominal GDP is just price times quantity..
In the real world, nominal GDP and the price index must be calculated first, and only then can real GDP be calculated.
Of course, it is hard to understand why there would be any exchange in a one good economy. What does the money price of corn really mean? Why are there any exchanges? Well, you can model overlapping generations. That makes money a saving vehicle. This means we ignore money's role as medium of exchange that is so important in the real world because there are many goods and resources. And further, in the real world, while money can be a savings vehicle, there are many other ways of saving that are usually much better.
Finally, we can imagine a Walrasian Auctioneer determining the real output of all the products using an arbitrary numeraire. And all output and resource use is determined. Presumably, we could measure real GDP using any good as numeraire.
Then, after that is done, the Walrasian Auctioneer could call out money prices to equate the quantity of money and the demand to hold money. We can even imagine that money is fully neutral,, so that every money price is proportional to the numeraire price.
So, real output is determined, and the price level is determined. Nominal GDP is nothing more than the product of two independently determined things.
But the real world is a monetary exchange economy with many goods and resource. These goods and resources are sold for money. These goods and services are purchased with money.
And that is why nominal GDP--how much money is spent and earned--is not just a real thing that happens in the economy, it is also an important thing.
The actual prices and quantities of the various goods and services are also real things and important for many purposes. In a monetary exchange economy, the amount of money spent on and earned from each good is a real thing and important.
The price index and its rate of change, is not the same thing as the market price of a single good and its rate of change. And real GDP is not the same thing as the market determined output of a single good and its rate of change.