The NGDP gap is equal to potential NGDP minus actual GDP. If the economy is operating below potential, the gap is negative. If it is temporarily operating in boom mode, above its sustaiable potential, the gap is positive.
Market monetarists watch the gap because they think the level of NGDP is even more important than its rate of growth. If the gap is negative, the Fed should apply more stimulus until the gap closes. As you can see, if the desired long-run growth rate of potential nominal GDP is 5 percent (composed, say, of 3 percent real GDP growth and 2 percent inflation), then the NGDP growth rate will have to be faster than 5 percent for a while to catch up. Similarly, the Fed would apply monetary restraint to temporarily slow NGDP growth below the long-run norm in order to cool off an overheated boom.
(Parenthetically, it is worth adding that some of the stimulus or restraint could, in principle, be applied through fiscal policy. Market monetarists think monetary policy has to do most of the heavy lifting, but some other economists, especially those who adhere to modern monetary theory, disagree. Exploring that debate would take us far beyond the bounds of this post. The only thing you need to know is that you are liable to cause great offense to your closest friends in the economics profession if you get market monetarism and modern monetary theory mixed up.)
Economonitor — Ed Dolan's Econ Blog
Latest Economic Growth Data Give Cheer to Market Monetarists, or, What is the NGDP Gap and Why do we Care?Ed Dolan
According to MMT, the market monetarists have the story backward. Rising NGDP is a consequence rather a causal factor.
The Fed is unable to stimulate the economy through monetary policy, as QE shows as MMT predicted and explained, and the expectations fairy doesn't exist. The Fed saying that it is aiming at a specific increase in NGDP rather than an inflation target doesn't make it so. The Fed has no credible way to do this, and a negative interest rate won't do it either for reasons that MMT explains.
In the first place, like QE negative interest acts as a tax. Secondly, banks are not constrained in leading to credit worthy customers demanding loans that are profitable to banks after risk weighting. Banks cannot be forced to lend through monetary adjustments as MM assumes. There is no "hot potato" effect associated with the monetary base.
MM is based on the discredited quantity theory along with a faulty understanding of money and banking, finance, and the operational reality of the current monetary regime with respect to economics.
According to MMT analysis, the way to stimulate the economy is to increase aggregate demand through government spending, which may also lead to some increase in measures of inflation, i.e., an increase in NGDP. However, the resulting stimulus is projected to also increase investment in response to increasing demand, there by also increasing real GDP.
MMT has explained the transmission through fiscal policy and lack of transmission with adjustments to monetary policy including forward guidance (expectations fairy). MM still hasn't given a convincing explanation of a transmission mechanism other than the expectations fairy and the so-called hot potato effect.
So MMT and MM agree that NDGP is the desired outcome and getting there is worth accepting some inflation above the Fed's current 2% target. They disagree over the causality, however, hence the policy means.