In a recent podcast episode, I analyzed three different scenarios where today’s expectations about future economic conditions can affect supplies and prices in the near term. Specifically, I analyzed this mechanism for three different goods: (i) US fiat dollars, (ii) barrels of crude oil, and (iii) ounces of gold. I will devote each of these three blog posts to one of these goods. In this first installment, we’ll walk through the case of US dollars.
A Future Helicopter Drop
Suppose that, for whatever reason, the Federal Reserve announces that in exactly one year, it will double the quantity of USD by printing up $100 bills and dropping them from helicopters around the country. Would that have any effect in the near term?
Suppose we believed in a very crude, mechanical theory of prices—such as the famous equation of exchange, often written as MV = PQ. This type of approach can lead people into believing that increases in the money stock lead to a corresponding increase in P. Conversely, this equation might lead people to believe that a future influx of more cash can’t affect prices in the present.
But this is wrong. In economics, value is subjective, and that includes the value of money. Beliefs today can affect the valuation of money, and hence our hypothetical Fed announcement definitely has the power to causes prices to rise immediately. Even in the equation itself, a constant M can go hand-in-hand with higher P if we assume that velocity, V, increases. That’s exactly what would happen if people want to “dump cash.”
To unpack the process: Once the new information hits, people anticipate much higher prices in 12 months’ time. Therefore their current holding of actual money (such as currency in their wallet, or a checking account balance with a reputable bank) is suddenly too high, because the money now has a much worse expected real rate of return (measured in purchasing power). So everybody has an incentive, at the “level” of prices that prevailed right before the news broke, to try to trade away surplus cash.
All Money Must Be Owned By Someone At Every Moment
People can fall into a trap of viewing money “in circulation,” just bouncing around from wallet to purse. But of course, in reality anytime someone “dumps money” by trading it for some other goods or services, there is necessarily a person on the opposite side of the trade who is “accruing money,” who is—at that moment—deliberately enlarging cash balances.
So how does equilibrium get restored? If everybody initially wants to reduce his or her money balances, what changes to make the community as a whole willing to hold the same money stock that it held the day before?
The answer, at least in terms of how economists typically model these processes, is that we assume people ultimately pick their optimal cash holding by reference to its real value, i.e. its purchasing power. For example, suppose someone tries to maintain his finances such that he typically carries at least $100 in his wallet, which is only to be “breached” in rare situations and if so, he replenishes it quickly. Economists assume that the reason he picked $100, rather than $50 or $200, is that at prevailing prices, $100 buys the amount of stuff that he might want to obtain in a “spontaneous” purchase.
Armed with this insight, we can see how equilibrium is restored after the Fed announcement: Prices jump immediately (though not necessarily to the level they will attain once the helicopters drop their goodies). Even though the public may still consider the cash a more dubious asset to hold than was the case before the news, the higher price level means any given nominal stockpile of cash is now smaller in real (inflation-adjusted) terms. Thus the higher level of prices (from the sudden jump) is what makes the community willing to hold the same nominal quantity of cash as before.
Wait, Do Expectations Completely Neuter the Helicopter Drop?
The quick answer is no. Whatever people think of the money, it surely increases the public’s ability to spend it if the Fed doubles the quantity. Surely, doubling the quantity of money should cause a noticeable change in the macroeconomy.
A longer answer is still no, but the reasoning is more sophisticated: During the transition period, which occurs after the Fed announcement but before the actual money drop, it must be the case that prices are continuously rising. This is necessary to make people willing to hold the smaller stock of money in the interim period, and hold the larger stock of money after the helicopter drop.
The Price Inflation Rate Must Be Increasing Throughout the Transition
We can go even further. Not only must prices keep rising throughout the transition—i.e., the rate of price inflation must be positive—but the inflation rate itself has to steadily increase throughout the transition.
The reason is that at each new height of the price level, the original stock of money M now translates into a smaller real cash balance per capita. To induce people to want to hold the smaller (real) cash balance, the expected future depreciation of the cash must be higher. So that means all along the transition path, it must be the case (in equilibrium) that prices are rising at an increasing rate, because the accelerating prices hikes are yielding the necessary drops in money’s purchasing power.
At this point, rather than try to describe the outcome with more and more words, it will be more illustrative to give a specific example.
A Simulation
Let me stress that the following is not a robust model of money and inflation. Rather, I’m just sketching out the results of a mathematical application of the framework discussed in the previous section.
Specifically, assume that the original money stock M, as well as the parameters we set for the equations governing money demand etc., are all picked such that originally, the community holds M while prices remain steady, i.e. a zero (price) inflation rate.
Now at time A the Fed announces that after a certain duration, at time D the money stock will double to 2M. Assume from that point forward, prices are once again stable, i.e. price inflation is zero again. Further assume that the parameters are such that, when the news initially hits, the price inflation rate immediately jumps to 10%, and that it steadily rises to meet 100% right at time D.
The following charts show what must happen (given our framework and assumptions) during the transition period (between time A and time D).
The blue line shows that the price level jumps a little more than 7 percent immediately upon the Fed announcement. It then rises (at an accelerating rate) to reach double its original value just as the new money is dropped at time D. After that, it stays flat.
The red line shows that the inflation rate starts out at 0 percent (i.e. stable price level) and then jumps immediately to a 10% rate. The inflation rate itself steadily rises during the transition period, maxing out at 100% at time D. Yet at that moment, the inflation rate drops back to 0 percent, where it remains.
After prices have doubled, they have exhausted the full impact of the helicopter drop.
Two Tweaks to the Assumptions
Again, within this particular mathematical model, we can chart what happens if we announce the same doubling of the money stock but it will happen in half the duration. Or, we can chart the impact of keeping the same duration, but now having the money drop bring the total to 4M rather than 2M. We provide the results below:
(In these updated charts, time D’ occurs at the midpoint between A and D.)
As the new charts show, if the same doubling of the money stock is expected in half the time (i.e. the dashed red lines), then the price level still doubles. But because it must do so in half the time, the inflation rate is higher throughout the (shorter) transition period.
On the other hand, if the duration is the same but the Fed is expected to quadruple the money stock (i.e. the dotted green lines), then the inflation rate is exactly double the baseline, at every moment during the transition. The price level in this scenario maxes out at 4P, after which it stays constant.
Conclusion
To reiterate, I am not arguing that the above money math model should be taken too seriously. Rather, it serves as a plausible way to organize our thoughts and avoid contradiction.
In this first of three posts, here are the important takeaways: (A) Future expectations can affect the demand for money today, and hence can cause prices to rise today. (B) If we make plausible assumptions about the interaction of price inflation with money demand, then we conclude that prices must be rising at an accelerating rate during the transition, before the expected new money has actually hit.
Dr. Robert P. Murphy is the Chief Economist at infineo, bridging together the dependability of Whole Life insurance policies with the benefits of blockchain-based finance.
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