I mentioned earlier that I would discuss how the historical theoretical framework of economics would look if the information transfer model was correct in a post; this is that post.
From the point of view of information transfer economics what we should see is a pre-Depression vogue for quantity theories of money (since the information transfer index $\kappa$ would be low, on the order of $\kappa \sim 0.5$, which means the quantity theory is a good description) that drifts into interest rate theories as the quantity theories lose their power (an interest rate description is not necessarily affected by the unit of account effect). Then would come the Depression in the 1930s and theories where monetary policy loses any effectiveness as $\kappa \rightarrow 1$. While previous recessions would have been "V"-shaped, appearing mostly monetary in nature since $\kappa \sim 0.5$, this would begin a "U"-shaped depression. After the depression would follow a resurgence of quantity theory as $\kappa \sim 0.5$ (likely with a revisionist bent towards why quantity theory failed in the Depression). Again these would lose power and give way to interest rate-based theories and "U"-shaped recessions starting in the 1990s as $\kappa$ increases. Finally economic theory would culminate in a resurgence of Depression-era theories as $\kappa \rightarrow 1$ in the late 2000s. This path of the information transfer index $\kappa$ looks like this one below (from this post):
So how well does this picture work? Stunningly well.
Fisher published The Purchasing Power of Money in 1911 (containing the equation of exchange) and the "Cambridge school" put forth their quantity theories of money in the 1920s. Keynes published his Tract on Monetary Reform in 1923 (Brad DeLong called it the best monetarist book ever written). In these cases, M1 was the aggregate of choice but when $\kappa \sim 0.5$ M1 is parallel to MB in logarithm (differing by just an overall scale factor). As $\kappa$ increased, Fisher moved on to interest rates in his magnum opus The Theory of Interest in 1930. Keynes published his General Theory in 1936 which contains the guts of the IS/LM interest rate model and showed how it was possible for the economy to be mired in a "liquidity trap". Keynesian theory took over the economic mainstream. However, since the Keynesian view concluded that the money supply doesn't directly affect inflation (it had been developed in an environment where $\kappa$ was large, thus this was an empirically true relationship at the time and had been for decades before). Concentrating on unemployment, the lack of focus on inflation in a low $\kappa$ environment would lead to inflation. The Keynesian theory would remain a relatively accurate description of the economy as long as interest rates remained above zero. Recessions were "V"-shaped after the war.
However, as inflation increases in the information transfer model, the quantity theory becomes more accurate. Friedman and Schwartz published A Monetary History in 1963. They put forth the revisionist monetary theory that it is M2, not MB or M1, that controls the economy (it is more likely M2 dropped in response to the Depression than caused it). As $\kappa$ approaches its lowest value in the late 1960s and 1970s, inflation gets bad enough to cause a paradigm shift. The Philips curve breaks down because the quantity theory explains the price level (since $\kappa \sim 0.5$), not unemployment. Lucas issues his critique in 1976. The Fed even claims to try Friedman's idea to target M2, but it is far too unstable since MB controls the price level (in the information transfer model) and M2 is derived from it by the private banking sector hence contains a "business cycle" component -- which is why it dropped during the Depression. The Fed is given its dual mandate in 1977 to control inflation and unemployment. The Fed decides to cause a serious recession, raising interest rates starting in the late 70s in order to control inflation. It is a success (because $\kappa \sim 0.5$) and monetary policy becomes a prominent component of macroeconomic stabilization.
As the information transfer index continues to increase, the direct relationship between between the price level and the money supply begins to fade again. Plus there were all the old Keynesian successes to understand (or revise)! Rational expectations based theories enter the field. Monetary policy no longer controls the empirically estimated price level, but instead controls the "expected" price level. Keynesianism plus NAIRU or monetarism plus interest rates dominate "saltwater" and "freshwater" economics respectively, essentially interpolations between the $\kappa \sim 1$ and $\kappa \sim 0.5$ information transfer theories (the former expands around $\kappa \sim 1$, while the latter expands around $\kappa \sim 0.5$). This is somewhat successful and we get "the great moderation", but "U"-shaped recessions have returned starting in the 1990s. The Fed doesn't cause recessions with monetary policy as it used to. Japan reaches $\kappa \sim 1$ earlier than other major countries and stagnates with respect to monetary policy. Krugman writes in 1998 about the return of the liquidity trap. In the late 2000s, the US is back near $\kappa \sim 1$ and we get Krugman's "return of depression economics" and the Keynesian liquidity trap. Interest rates are at zero. Large increases in the monetary base do little to the price level. New "market monetarists" (aka "monetarists") like Scott Sumner claim that monetary policy can put the economy back on track if central banks manage expectations correctly and/or change from interest rate targets to higher inflation targets or ideally NGDP targets. (As there is no measure of inflation expectations that differs significantly from empirically measured inflation, I personally don't see how inflation expectations could explain anything empirically measured inflation isn't explaining. Why are expectations different from market forces? )
Of course, different market-based targets or expectations management will not work according to the information transfer model. Keynesian stimulus might work. Accelerating inflation is a possibility. However, what appears to have accomplished the exit from $\kappa \sim 1$ was exiting the gold standard. This caused a phase transition, redefining the monetary base.
The following graph illustrates the preceding account of economic history; it shows the monetary base (dark blue), M2 (light blue and dashed), and the price level (green) over the past several decades. The prominence of the quantity theory of money happens right when these three lines become parallel (gray region, $\kappa \sim 0.5$). On either side of it, the direct relationship between the measures of the money supply becomes murky since $\kappa \sim 1$. We can see the "V"-shaped recessions happening at low $\kappa$ and $U$-shaped for high. We can see the problem that quantity theories had with MB increasing during the Depression and the revisionist view that M2 is responsible. We can see where inflation expectations come into vogue as the price level falls away from its direct dependence on the MB as $\kappa \rightarrow 1$. Most of all, we can see (as red bars) the three major macroeconomic events of this and the last century and how they occur when $\kappa \sim 1$ (the Great Depression of the 1930s), $\kappa \sim 0.5$ (the Great Inflation of the 1970s) and when $\kappa \sim 1$ again (the Great Recession of the late 2000s).
Compare the shifting paradigms in economic theory with these fits (red, blue) to the price level (gray dashed curve) in the information transfer framework that operates over all values of $\kappa$:
 There is a glib answer (proponents of expectations based theories are attempting to make up for the fact they are not using an information transfer model) and a less glib answer (proponents of expectations based theories are attempting to fix monetarism and allow it to explain difference between the times when quantity theories work like the 1970s and when they don't work like the 1930s and 2000s).