Tyler Cowen refers to the difficulties central bankers face in interpreting recent inflation and unemployment data. The trade-off between inflation and unemployment as described by the Phillips Curve no longer provides reliable signals. The drop in inflation experienced in 2009 was tiny compared to the dramatic rise in unemployment. Then, as unemployment declined by half over the next 6 years, inflation failed to budge with core CPI averaging 1.6% since 2010 (Chart 1).
This leaves policy makers at a loss - unemployment has declined substantially and real GDP growth has been slightly above 2%, but there has been no inflation in sight. Furthermore, recent volatility in equity markets, the prospect of a stronger dollar, collapsing commodity prices and a stagnant global economy underscore deflationary pressures. The timing and pace of policy normalization are basically unchartered territory. The aggregation error framework, which points to the velocity of bank money as the proper guide for monetary policy, can help untangle this puzzle.
The aggregation error framework is a re-interpretation of the quantity of money identity whereby velocity is a measure of ex-ante money demand and the aggregation error is a measure of disequilibrium between ex-ante money supply and demand. This represents a shift in perspective in regards to the quantity of money identity. The causality in QP=MV flows from MV with prices and employment being the residuals . Velocity is probably the most misunderstood macro variable. It has nothing to do with the speed with which money circulates in the economy. As money is a liability that can be created and redeemed in the same period, such speed of circulation could be infinite . Velocity is truly a measure of money demand. In particular, the velocity of bank money can be used as a proxy for the exchange money motive .
Chart 2 shows Bank Money Velocity in the US going back to 1959. The long-term trend can be derived by regressing such velocity against private leverage and the degree of bank intermediation resulting in 71% R Square. Short-term fluctuations in velocity are caused by the aggregation error. Velocity above trend means that base money exceeds asset money demand  indicating loose monetary policy and a positive aggregation error. Under such conditions the economy performs above expectations and prices rise. Velocity below trend means a shortage of base money indicating tight monetary policy and a negative aggregation error. The economy performs below expectations and prices decline.
High bank money velocity in the 1960s offers evidence of loose monetary policy which ultimately led to the collapse of the dollar-standard under Bretton Woods. In the 1970s agents continued to seek the safety of gold to satisfy their asset money demand which gave rise to stagflation. During that period, the aggregation error was determined by the supply of gold which was beyond the control of the Federal Reserve. In other words, agents held dollars in order to accommodate spending but not as a store of long-term wealth. This is evidenced by a pretty tight fit between actual and regressed money velocity observed in the 1970s. The 1980s brought tight monetary policy which re-established the dollar as a monetary reserve capable of satisfying asset money demand. This ended the stagflation pattern of the prior decade and created the policy space, which allowed the Fed to engage in active monetary policy during the period of inflation-targeting. Loose monetary policy as indicated by above-trend velocity powered the boom cycles of the 1990s and 2000s.
In the aftermath of the Great Recessions, time preferences took a tumble into negative territory. Interest Rates followed suit reaching the zero lower bound. Under such conditions, the Fed can prevent a negative aggregation error by expanding the monetary base but is unable to generate a positive aggregation error as agents with negative or zero time preferences are indifferent between holding their long-term savings in the form of money or financial assets. The fact that bank money velocity has closely matched trend offers clear evidence to that effect. In the absence of aggregation error, the economy has performed according to expectations with little to no inflation. In other words, over the last six years the Fed has engaged in neutral monetary policy, and tightening is not justified at this point.
It is important to note that an economy performing to expectations does not mean full employment. Expectations, as measured by the time preferences of private agents, can be depressed for variety of reasons most notably excessive debt. This is exactly what we are experiencing today as time preferences are depressed by the excessive burden of debt piled-up over 20 years of inflation-targeting.
Next, I will try to explain why the Phillips Curve is broken. According to the aggregation error framework, there is no trade-off between inflation and unemployment as both are residuals of ex-ante money supply and demand. The observed Phillips Curve is simply a by-product of the monetary regime. If domestic agents accept domestic currency as a monetary reserve capable of satisfying their asset money demand and the aggregated time preferences in the economy are positive, the Phillips Curve will show a negative correlation between inflation and unemployment. Under such conditions, an excess supply of base money over asset money demand results in a positive aggregation error causing the economy to perform above expectations and prices to increase. Conversely, a shortage of base money results in a negative aggregation error causing the economy to perform below expectations and prices to decline. This interpretation is consistent with the economic record under the Gold Standard and the period of inflation-targeting dubbed "The Great Moderation".
If the time preferences of private agents are negative or equal to zero, the central bank can prevent a negative aggregation error by expanding the monetary base as to satisfy rising asset money demand, but it cannot generate a positive aggregation error as agents with negative or zero time preferences are indifferent between holding money or financial assets. In the absence of aggregation error, the economy performs according to expectations and the price level is unchanged. Under such conditions, the Phillips Curve will not show any correlation between inflation and unemployment, which is what we have observed since the Great Recession hit in 2009.
If domestic agents do not perceive the domestic currency as a monetary reserve capable of satisfying their asset money demand, the central bank will not be in position to engage in counter-cyclical monetary policy. Instead, monetary conditions and the business cycle are dictated by foreign capital flows and domestic capital flight. This gives rise to a positively-sloping Phillips Curve with the 1970s being a great example. Even today many emerging and developing markets continue to face the double scourge of high inflation and high unemployment due to domestic capital flight and fickle capital flows from abroad.
 As the supply curve is fixed ex-ante, businesses can respond to a change in aggregate demand in the current period only by changing prices and employment.
 Imagine a world without money. Instead, agents use credit cards to accommodate transactions. Credit card balances are then paid-off upon receipt of income.
 This assumes that banks duration-match their assets and liabilities, which they are required to do by bank regulators in order to manage interest rate risk.
 Asset money demand represents long-term savings held in the form of money by agents who expect stagnant or declining incomes. Please refer to the post on time preferences for more detail.