In the first installment, I claimed that Old Keynesian consumption functions which give consumption as a function of current and a few lags of personal disposable income and wealth outperform models based on intertemporal optimization and that investment (to the limited extent it can be modeled and forecast) is mostly fit by GDP growth with a significant effect of estimated real interest rates on residential investment. This means that I think closed economy models of aggregate demand from 1970 (really roughly from 1936) are much superior to later models.
Now I am going to go all the way and write that I think the best available model of aggregate supply is the 1960s era Phillips curve. First it is necessary to stress (again) that this was an expectations augmented Phillips curve. It differed even from more recently used a-theoretic Phillips curves, because anchored expectations were allowed.
To close the model it is necessary to have both a wage Phillips curve and a price inflation Phillips curve.
This is just exactly the model which was considered to be most thoroughly refuted in the 70s. The failure was the justification for the complete change in methodology. But I don't think it failed at all. The straw man of an expectations un-augmented Phillips curve was knocked down, but it hadn't been set up by old Keynesians in the 60s.
Notably, Paul Krugman is convinced that old Keynesian views on the Phillips curve have been vindicated writing "Tobin was right" also at length here. Blanchard recently wrote The US Phillips Curve: Back to the 60s which, I should stress asserts that the pattern of inflation and unemployment has become similar to that of the 60s and not that theory should return to 1960s theory (or 1960s absence of theory if you prefer).
The very old point as recorded in undergraduate macro textbooks (and for decades nowhere else) is that all macroeconmists really need from the supply side is a model of inflation. That combined with an empirical monetary policy rule (I guess just a Taylor rule) yields the one variable needed to estimate aggregate demand and output.
The fact is that extremely old fashioned Phillips curves actually worked rather well through the 1980s. They were abandoned because of oil shocks, theoretical arguments, straw man rhetorical tricks and fashion.
I think there are two necessary changes that were (and are) to be made. First the 1960s era Phillips curves went too far in correcting for expected inflation. It was assumed that there was nothing particularly special about 0% nominal wage inflation. In history it is very difficult to achieve actual reduction in nominal wages. It occurred in many countries during the Great Depression and in Greece recently, but even very high unemployment rates do not seem to be high enough to break through downward nominal wage rigidity. In the USA in the 60s this wasn't an issue so applied macroeconomists who focused on forecasting didn't discuss it much. Tobin in 1972 (and Solow in 1978) did.
Second, as argued by Solow and Samuelson in 1960, cyclical unemployment can become structural. This has been named hysteresis and it is clearly an extremely important issue here in Europe. In practice the first difference in unemployment matters much more for wage inflation than the level of unemployment.
The combination of anchored expectations and hysteresis means that economists got it backwards around 1980 -- fluctuations in unemployment lasted longer than fluctuations in inflation. The costs of policy makers' confidence that disinflation would be painful briefly but beneficial in the medium run were immense.
Anyway more thoughts here