Monetary policy in the NGDP Empire is dominated by the Island of Speculativa. They have decided that the price of gold should grow 2 percent a year. This results in the index number rising 2 percent per year. They have an inflation target!
Meanwhile, over in Autarkia, the farmers are generally increasing their productivity. Corn production is rising. But when the weather is bad, corn production can grow more slowly or even fall. Further, the substitution effect is greater than the income effect, so when the weather forecast is bad, the farmers plant less corn. Employment is lower and so the production of corn is extra low when the forecast is right and weather is bad as was expected.
With the price of gold and so the price index going up 2 percent a year, when employment is low and the production of corn is extra low, nominal GDP grows more slowly and sometimes shrinks. It almost appears as if slow growth of nominal GDP or decreases in nominal GDP are causing reduced production and employment.
Of course, nominal GDP is just the product of two unrelated things, and so, causes nothing. Weather and expectations of the weather are causing decreases in employment and real output.
But suppose the Sumneran Party becomes influential in Autarkia and proposes that the quantity of money be expanded so that the price of gold rises more than the magic 2 percent. The idea is that if index number rises faster, then nominal GDP rises faster. They have a confused notion that the more rapid increase in nominal GDP will convince the farmers to plant more corn (despite the expectations of bad weather) or even more crazily, assume that it will change the weather.
Well, they can't convince the monetary authority over in Speculativa to create money faster to get gold prices rising faster. No, they leave the union and become the independent Kingdom of Autarkia. They issue their own fiat currency. They no longer worry about the price of gold. No, they take the quantity of money and divide it by the quantity of corn produced. They call the quotient, the "price" of corn. Following the long settled practice in the other island, they calculate an index number based upon the first price calculated. Then they multiply the quantity of corn by the index, and call it Nominal GDP for Autarkia. (If you skip the index number step, nominal GDP is just the quantity of money. And even with the step, it is just an odd way of describing the same thing.)
Well, next time the farmers expect bad weather, the farmers plant less corn and when the weather is really bad, corn production is very low. The Sumnerans do raise the quantity of money so nominal GDP growth is stabilized. But the reduction in employment and production is the same as it ever was.
Because, of course, nominal GDP is just the product of real output and a price index. Right?
P.S. Maybe in Autarka, but not in the real world where people sell goods for money and buy goods with money.