The recession was caused by a severe AD shock, i.e. falling NGDP. If it had been caused by an AS shock then the recession would have been accompanied by higher inflation. It would really help if people started to think more in terms of NGDP.
For Scott, nominal gross domestic product (NGDP) is fundamental. To me, it is accidental. To me, what is fundamental is real output. Then we have prices for different inputs and outputs, which are set relative to one another, but which are expressed in monetary units. Finally, we have the average price level, which is an index of average prices expressed in monetary units.
I view the money supply as a very wiggly lever for controlling average prices. If the monetary authority pushes really hard for really long, it can get average prices to rise quickly. Then, if it wants to get prices to stop rising quickly, it has to pull really hard for really long in the other direction.
I do not think in terms of aggregate demand and aggregate supply. In fact, I have a very hard time teaching them in my high school economics class, because they make so little sense.
The story of aggregate supply is as follows: start with sticky nominal wages, and with stupid workers willing to supply unlimited amounts of labor at whatever real wage rate happens to prevail. Then if average prices go up, average real wages go down and labor demand goes up. Because workers are stupid, they supply the additional labor, and output goes up. Hence, the aggregate supply relationship--as prices go up, the willingness to supply output goes up.
The (Keynesian) story of aggregate demand is as follows: start with a fixed supply of money, and with stupid investors who think that the short-term nominal interest rate in the Fed funds market is a proxy for all interest rates, including real long-term rates. Then, when average prices rise, the ratio of the money supply to the price level falls, creating an excess demand for money, leading to a rise in short-term nominal interest rates, resulting in a rise in long-term real interest rates, resulting in declines in spending on long-lived assets, such as housing. Hence, the aggregate demand relationship--as prices go up, the willingness to demand output goes down.
The beauty of this framework is that you can explain anything. Did prices and output both go up? Obviously, aggregate demand must have shifted right, causing upward movement along the aggregate supply curve. Did prices go up while output went down? Obviously, aggregate supply must have shifted left, causing upward movement along the aggregate demand curve.
The virtue of the Recalculation Story is that it gets away from this AS, AD framework. It explains the recession as arising from frictions in reallocating resources away from an unsustainable industry structure. I would agree with Scott that the low rate of inflation during the recession is a sign that the Fed could have tried wiggling its lever harder to keep prices higher. However, my conjecture is that if Fed had pulled its lever really hard what we would have had was mostly higher inflation, with little or no improvement in output.