Sunday, August 24, 2014

Endogenous Money Growth and Prices: Pilkington's Says Equation of Exchange Does not Support Monetarist Case for Inflation

Phil Pilkington is convinced that inflation is not always and everywhere a monetary phenomenon.

First, he thinks that he's found the trick to monetarism.
The monetarists proper converted this identity into a behavioral equation. This equation ran as follows and should be read running from left to right:Fisher equation2Note two things. First, the fact that we have converted the “equal by identity” sign into a standard equals sign. This implies causality running from left to right. So, the left-hand side of the equation causes the right-hand side. Secondly, we have placed ‘hats’ on the velocity and quantity variables. This implies that they are to be thought of as fixed. Thus the equation reads: “The sum of prices is equal to the quantity of money”. We understand the sum of prices here to be the Consumer Price Index (CPI).
He misunderstands the claim. Prices are a function of the monetary base in the long run. This is proven empirically. In a world where there are zero transactions costs and perfect information, prices and output would always match the product of money and its velocity. Money exists because we do not live in a frictionless world with perfect knowledge, so this thought exercise is of little use unless it helps us to imagine the obstacles preventing market clearing and the means by which agents overcome those obstacles. One means is that prices lower. The other is that new moneys are created in response to increased demand for money in the broadest sense. More on that later.

Pilkington then goes on to disprove the quantity theory with some graphs.

Let us first lay these out in a standard graph form to see if we can intuitively spot any correlation. All graphs measure percentage changes year-on-year of both variables mapped. The reader can click on the image to enlarge it.
Money supplies vs. inflation
Conspicuously missing, the monetary base. Let me show you what that looks like compared to CPI to the monetary base.

***Note three things. 1) I left out the years since the crisis as the Federal Reserve has been sterilizing its own injections. 2) A first difference log transformation will show some correlation, but the correlation will be imperfect due to international demand for dollars and some endogeneity of Federal Reserve Policy. 3) The long run trend is important, which is why I show year to year changes in the second graph. Both measures appear to be following roughly the same long run trend.

I admit that in the microeconomic sense, Pilkington is right. Prices are not set with perfect knowledge, so sometimes they are set too high, and other times too low. If they are set too high, a surplus of goods is built up by the sellers. Likewise, if prices are too low, sellers liquidate their inventory before demand is satiated. In the first case, the problem can be alleviated by two means. Either prices fall or agents acquire sufficient funds to purchase the excess inventory.

Likely both happen. If firms are price searchers, then there are going to be times when they lead prices ahead of demand and others where demand leads prices. And there will be rare circumstances where the theoretical equilibrium price and the market price meet. Most of the time, there will be either too much or too little demand for money and, necessarily, gluts and shortages of goods. This promotes volatility in the broader monetary aggregates.

The broadest monetary aggregates expand endogenously. When prices are higher than the broader money stock merits, two things happen. 1) Prices eventually begin to fall and 2) agents still want to make purchases, so they attempt to acquire money by more costly means and employ assets less commonly used as money in exchanges (i.e., asset swaps). In fact, we can imagine a theoretical monetary aggregate that includes everything used as money that is built on top of the base. Let's call it, the total money stock - Mt. I expect that this aggregate and prices would tend to oscillate around one another. If this is the case, then we would have a circumstance where the price level - the theoretical construct, not some price level built ex post - affects the money stock  much like the money stock affects the price level. The time taken between events where the market reserve ratio is equal to the natural reserve ratio - the ratio of base money to broader money that would be reached if all pareto improvements could be made -  cannot be ascertained theoretically. It is an empirical question.

The long run level of prices is determined by three things. The size of the monetary base, the natural reserve ratio, and velocity per time period. For analysis, we can hold velocity constant. The ratio of base money to broader money will tend to oscillate around this natural ratio as deviations to far from it will lead to losses. That is, if ever reserve ratios become too far below or too far above the natural ratio, banks and other financial institutions must allow their reserve or capital ratios to rise or else risk insolvency. Those banks that don't adjust in a timely manner go out of business.

My exposition leads me to a second principle as well. The growth rate of Mis a function of the expecation of P*y. If actual nominal GDP is lower than expected nominal GDP, there is an output deficiency. This follows from Say's law. If their is excess demand for money, then there is necessarily a surplus of goods due to their prices being above the market clearing price. This excess demand for money will be offset by the creation of purchasing power in the form of fiduciary currency or anything else used as money. The process can be described below.
1) Prices of goods are higher than money balances merit
2) Demand for money rises
3) New moneys and quasimoneys are created // prices begin to fall
4) Economy returns to long run growth path.
 (Both events in 3 occur simultaneously.)

Finally, we do not have a measure for the broadest money stock. The broadest money stock is difficult to measure because its definition must always expand to include brand new types of moneys. I'm happy to hear suggestions about which already constructed aggregates are most representative.


  1. Monetary base vs. CPI.

    I left this out because I assumed that everyone knew that they had no relationship to each other (especially after QE!).

  2. James,

    A few quick thoughts:
    1) I don't believe it can be proven empirically that "prices are a function of the monetary base in the long run." Aside from issues of determining an appropriate price level and long-run period, the empirical data merely shows correlation, not causation in either direction.
    2) In your graphs you leave out the post-crisis years and refer to central bank sterilization. Does this imply that "prices are a function of the monetary base" only when certain conditions hold? If so, what are those conditions?
    3) Say's law, at least as outlined here, appears to assume a certain structure to the economy in which there are only two goods (money and non-money goods) and the excesses of supply and demand can be effectively transmitted across time (unless you're assuming a one-period model). Alternatives of these assumptions are considered, at length, in Axel Leijonhufvud's book, On Keynesian Economics and the Economics of Keynes.

    Overall I think the different conclusions arise largely from applying economic models with different underlying assumption. Both theories can therefore be "correct," given certain assumptions, and both may be useful, depending on the intended purpose.

    1. Josh,

      Thanks for your thoughtful response.

      1) According to the accounting definition, prices move for 3 reason. Changes in the money stock, changes demand to hold real cash balance, or changes in output.

      The trouble is endogeneity of monetary policy. For example, if price level stabilization is the policy goal, increases in the base will not correlate as closely with increases in prices. To some extent, this makes changes in monetary base of function of changes in the prices level. If monetary policy was not endogenous, then we can expect that the traditional monetarist formulation will hold.

      2) Beneath the graph, I note that fed sterilization of its own increases in the base have changed this relationship. To be more explicit, velocity of the base has plummeted.

      3) Thanks for the suggestion. I've read an article from that book before. I'll have to order it! My description is operating in the present, but I have not excluded forward looking plans. For example, if an individual increases his debt employing unleveraged collateral during a period of dear money, he has responded to an environment of tight liquidity by finding a source of funds that he might not otherwise use. He must be able to repay that debt at some later date and expects that future proceeds will allow him to do so. These credit adjustments help compensate for deficient AD.

      I'd like to learn more about these different "economic models with different underlying assumption[s]." Do you have any suggestions?

  3. James,

    I'll reply in the same order:
    1) It would be equally correct, based on the accounting definition, to state that changes in the money stock, changes in demand to hold real cash balances, and changes in output all move because of changes in the price level. Any variable in the equation can initially move for an infinite number of reasons. The equation merely states that if one variable changes at least one other variable must change as well.

    A behavioral assumption may be that price changes are always caused by changes in the other three variables. To the degree that this represents a Monetarist view, and that the latter two variables are assumed constant, then the traditional formulation holds by definition (regardless of monetary policy).

    2) This reasoning seems to imply the Fed can control V. Since velocity is typically assumed constant in the long run, at what point should we expect velocity to return to its previous levels? If velocity is not expected to return, is it fair to say that monetary policy can affect V in the long run?

    3) You mention that the borrower "must be able to repay that debt at some later date." This appears to preclude default. What happens when defaults occur, as they inevitably do in the real world? Do defaults matter?

    Separately, I was referring to what I believe is Clower's distinction between notional and effective demand (based on Keynes?). As I understand it, the decision to postpone consumption today creates an excess notional demand for consumption in the future. Forward markets, however, do not exist in our present world to perfectly transmit information to producers about the specific time and place that consumption will take place. From the perspective of present producers, the effective demand for goods, upon which they base investment decisions, is therefore reduced.

    As for models with other assumptions, Phil is seemingly better read than I. Off the top of my head I don't have specific articles (or books) but Basil Moore and Paul Davidson are good on Post-Keynesian views. George Soros' theory of reflexivity is another type.

  4. Josh,

    1) I'm not denying that price can affect the other variables. But, it depends on how you mean. Prices can affect the base money stock if either the central bank sets changes in M at all in reference to changes in P. If policy is not a function of changes in prices, then the effect will be one way.Or, under a commodity standard, excess demand for prices, which occur when prices are sticky downward and there has been a negative shock to AD, will encourage the production of the commodity base money. If the stock of money fails to adjust to compensate for sticky prices in a scenario where velocity has shifted, then y takes the hit. I didn't mean to suggest that I didn't believe this was the case.

    2) The Fed does not control V of the monetary base, but it does influence it. While I'm tempted to blame the drop in velocity on the Fed's payment of interest on reserves, however, the growth rate of the effective monetary base - that part of the base not sitting in the vaults of the Fed - has remained relatively constant during the last 6 or so years. I have a hard time believing that the Fed could accomplish such accurate sterilization with such a blunt tool. That said, if it is not only interest paid on reserves that have encouraged banks to hold onto base money, I don't know what other major factor is at play.

    3) Of course default is an option. This actually creates problems for the endogenous creation of money during the beginning of a downturn. This is when risk is at its highest, so banks are far less willing to lend. Only once volatility lowers and borrows are willing to pay a mutually amenable price for liquidity does that scenario change. In any case, the exchange occurs with the expectation that default will be avoided or occur at some manageable rate among borrowers.

    Technically, effective demand, though made famous by Keynes, was first developed by Ralph Hawtrey in in Good Trade and Bad. I suggest reading David Glasner's working paper on this topic. I'll have to spend some time thinking about reductions in effective demand due to deferment of consumption. As with any positive transaction cost, this information asymmetry - or might it be a lack of information altogether aside from subjective probabilities assigned by each party - creates an opportunity for entrepreneurs to estimate this information. This is the role of the speculator, no?

    Thanks for the suggested readings.

  5. James,

    Thanks for the pointers on Hawtrey and Glasner, as well as encouraging me to reconsider my point of view.

    My point in the first part was simply that an accounting identity, by itself, does not contain any causal implications. The different responses you discuss may all be valid but they entail adding behavioral (causal) assumptions to the equation of exchange. Furthermore, those causal assumptions rest on countless other assumptions such as the type of competition. Whether or not one's chosen set of assumptions is relatively better suited for a given task is, in my opinion, forever up for debate.

    On the second topic, one might argue that (effectively) zero interest rates on most other short-term financial assets is behind the decline in base velocity, irrespective of interest on reserve balances. Separately, I personally find your terminology in this section a bit confusing. Am I correct in interpreting the effective monetary base as currency outstanding, including currency held in bank vaults? Also, is it correct to interpret vaults of the Fed as a metaphor for deposit accounts at the Fed?

  6. Josh,

    You've uncovered my bias toward economic history, as opposed to pure economics. The quantity theory is always subject to interpretation of the circumstances surrounding changes in the variables. Perhaps I misinterpret Pilkington's argument, but he seems to be claiming that the monetarist interpretation of the equation of exchange is altogether incorrect. Friedman expressed his view in the 70s when inflation was an imminent problem. In any case, I think it holds best for changes in the base, but I admit that the correlation is not perfect because of inflation targeting.

    My apologies on the terminology. I spend most of my time studying older Fed policy, so I can be sloppy in this regard. Good point about zero rates. When risk is taken into account, leaving money on account at the Fed is better than investing it. Still, I feel like something is missing from this story.

    So are you comfortable blaming the drop in velocity of the base on IOR?

  7. James,

    I share your bias so that's good to know. I can't/won't speak for Philip but my issues with the monetarist interpretation are that it often (implicitly) minimizes any institutional considerations and leaves open the question of how long is the long run (~10 years? ~100 years? ~1000 years?). The former is not necessarily an issue from a purely forecasting perspective but, in my opinion, is a significant issue with regards to informing monetary policy.

    If we're discussing monetary base velocity, I am actually closer to the zero rate camp. Since reserve requirements are not binding, the primary purpose of reserve balances is settling interbank balances. For excess reserve balances, the opportunity cost of holding other assets is therefore of the utmost importance.