Believe those who are seeking the truth. Doubt those who find it. Andre Gide

## Monday, July 26, 2010

### Interpreting Recent Movements in the Money Supply and Price-Level

In my previous post, I noted how the Fed has recently doubled the supply of base money. At the same time, the price-level (however measured) has shown no correspondingly dramatic change. This led me to question a simple version of a popular theory of the price-level; the so-called Quantity Theory of Money (QTM).

Maybe I was a little too hasty. After receiving several thought-provoking comments on that post, I am led to re-think what I was trying to say. The basic idea is that new money used to purchase assets (a la the Fed's MBS purchase program) need not have any price-level effect -- even if the increase in the money supply is permanent.  On the other hand, it seems that it is also possible to square the observed phenomenon with a conventional QTM. Below, I discuss both interpretations.

A portfolio choice model

To sharpen the discussion, let me write down a simple model. The technology governing the return to capital investment works as follows. Let k denote capital investment at date t. Then the return to this investment is realized at date t+1 and is given by   z+ f(k), where f(.) is strictly increasing and concave (diminishing returns to investment) and z+ denotes the realization of a productivity shock.

Let ω denote information available at date t that is useful in forecasting future productivity z+. I like to refer to ω as news. Let E[z+|ω] denote the conditional forecast over future productivity. Hence, for a given level of domestic investment k, the expected return to an additional unit of investment is given by the expected marginal product of capital, E [z+|ω]f  ' (k).

Assume that there is one other asset in this economy: government money/debt (I make no distinction here). Let R denote the gross nominal interest rate paid on government money (think of the interest currently being paid on reserves by the Fed).  Assume that R is a policy parameter and that it is held fixed over time; net interest on maturing debt is financed with lump-sum taxes.

Let p(ω) denote the price-level at date t (I write it this way because I anticipate that the equilibrium price-level may depend on news). The (gross) rate of inflation is defined by
Π(ω+,ω) = p+) / p(ω).

If agents are risk-neutral (assume this is so), then for both capital and money to be willingly held in the wealth portfolios of individuals, the following "no-arbitrage-condition" must hold:

[1]  E[ z+ | ω]f  ' (kd ) = E[ R / Π(ω+,ω) | ω]

The LHS of [1] is the expected marginal product of capital and the RHS is the expected real return on government money. Condition [1] implies that investment demand kd is decreasing in R and increasing in (expected) inflation.

Let y denote aggregate saving which, in what follows, I view as a parameter (this allows me to focus on the forces that determine the composition of saving, rather than its level). Consequently, the demand for real money balances is determined residually by qd = ykd.

Market Clearing. If M is the nominal supply of base money at date t, then market-clearing implies that M = p(ω)qd(ω) must hold at every date. At date t+1, this implies M+ = p+)qd+).  Assume that the money supply grows at a constant rate μ, so that   M+M. (Let the new money is injected by way of helicopter drops). It follows that the equilibrium inflation rate must satisfy
Π(ω+,ω) = p+) /p(ω) = μ[qd(ω) / qd+) ]. Now, combine this expression with [1] to form:

[2] E[ z+ | ω]f  ' ( yqd(ω) )qd(ω) = (R / μ)E[ qd+ ) | ω]

Given a stochastic process for news, condition [2] can be used to solve for the unknown function qd(ω).

Simplification: Actually, most of what I want to say here can be gleaned from the simplified case where we just shut down the aggregate news shock (nevertheless, I think it is useful to keep the underlying stochastic structure in mind). In this case, condition [2] reduces to

[3] z f  ' ( yqd ) = (R / μ)

Interpretation. I like to think of this model as capturing an element of banking (or of intermediation, in general). The bank (consolidated banking sector) must decide how to allocate its deposits y between cash q and loans that finance private sector capital spending k.

Under this interpretation, the nominal value of "bank money" is given by pk. From this, we may then construct a broad money aggregate as the sum of government money and private money, M1 = M + pk. Exploiting the market-clearing condition p = M / q, we may rewrite this latter expression as:

[4] M1 = [ 1 + (k / q)] M

The term in the square brackets in [4] is the so-called money multiplier (M1 / M). Note that the money multiplier here is endogenous; it depends on the loan-to-cash ratio (k / q), which is determined by the banking sector in relation to prevailing macroeconomic conditions. [You can verify that p = M1 / y as well].

1. An asset purchase program

O.K., so here is what I had in mind vis-a-vis my earlier post. Consider equation [3] and hold all parameters fixed. Then the equilibrium price-level is determined by pt = Mt / qd  (The demand for real money balances remains constant in a stationary equilibrium -- all nominal quantities expand at the same rate as base money...a very QTM result, by the way).

What is important to realize here is that the price-level is pinned down by the ratio of the supply and demand for fiat money. While it is also true here that  p = M1 / y, the price-level depends on M1 only to the extent that the supply and demand for fiat money influences M1 (i.e., via equation [4]).

Now, imagine that the Fed surprises the market by printing up some new money, using it to purchase some private sector capital (MBS). To my way of thinking of things, the new money created in this manner does not alter the supply of fiat money--even if it does increase the supply of government money. Since the supply/demand conditions for fiat money remain unaltered, the price-level remains unchanged.

Note that in this operation, the supply of private money falls by the amount of the Fed purchase, so that M1 remains unchanged. All that has happened here is a relabelling of the currency (the Fed is simply acting like a private intermediary). Prior to the experiment, the total supply of private (backed) money was pk. Imagine now dividing pk into two components: private money and government backed money. An econometrician will observe an increase in base money supply accompanied by disintermediation in the banking sector. But a rose by any other name is still a rose. [rose = backed money].

2. A flight to quality

In the view of some, a recession is caused by a sudden "excess demand for the medium of exchange." I interpret this to mean an exogenous increase in the demand for government money/debt.

Of course, as someone cast in the "New Monetarist" mold, I am not inclined to believe in exogenous money demand shocks. People do not, in my view, simply wake up one morning en masse wanting more cash or government treasuries. Well, maybe they do. On the other hand, I do not think it far-fetched to imagine that any change in money demand might not be driven by something more fundamental.

The fundamental shock I want to consider here is "bad news." That is, assume that E[ z+ | ω] is increasing in ω, so that a high realization of ω corresponds to "good news" and a low realization of ω corresponds to "bad news."

What typically happens near a cyclical peak is the arrival of information that leads private sector actors to revise downward their forecasts on the return to additional capital investments (e.g., new residential structures). A part of the information flow might take the form of rising foreclosure rates, for example. In any case, the point is that the sudden arrival of bad news leads to a form of rational pessimism.

What are the implications of a bad news shock in the context of the model developed here? Properly, we should study [2]. But it turns out that the basic intuition can be gleaned equally well from [3] and interpreting an exogenous decline in z as a bad news shock.

Mechanically, condition [3] asserts that the real demand for government debt qd is decreasing in z. This follows from the strict concavity of f(.). So a decrease in z leads to an increase in qd; an econometrician is likely to identify this event as a positive money demand shock.

Intuitively, bad news leads banks to rebalance the composition of their assets--they want to contract their lending activities (the forecasted returns are no longer as attractive) and they want to substitute into higher grade government money/debt--there is a "flight to quality." The consequent increase in money demand is deflationary (in  the model, there is a sudden drop in the price-level). Recall: pt = Mt / qd .  The contraction in bank-lending leads to a subsequent drop in (expected) GDP, owing to reduced levels of investment today.

Note that the decrease in (k / q) here results in a decrease in M1 and the money multiplier, even for fixed base money supply M; see condition [4]. Needless to say, this effect (disintermediation) seems present in the data.

Now, according to this interpretation, the decline in the price-level was avoided by recent Fed actions. In particular, the Fed increased the supply of (interest-bearing) fiat money to accommodate the apparent increase in demand for these government liabilities. Note that, according to this view, the Fed had better stand ready at some point in the future to reverse its money injection, if a huge increase in the price-level is to be avoided (once good news returns, and private investment demand picks up).

Concluding thoughts

I'm not sure which interpretation I like better. It is possible that both interpretations contain an element of truth. You tell me (maybe you think both models are lousy).

Let me address what I think will be one sure criticism. The model I use above makes no distinction between government money and debt. To put things another way, money is treated simply like any other asset. In fact, money--in the form of cash--is special; it is a medium of exchange. The model here simply views money as a store of value.

Well, the first thing I would say in response to this is that at least my model has money! (unlike, say, conventional "cashless" NK models). And anyway, the money/debt object in my model does circulate as a medium of exchange. In the OLG model, for example, the asset passes from one group of agents to another in a sequence of spot exchanges. I might further add that the existence of government money/debt is welfare-improving in the model (of course, I have not modeled the government as potentially exploiting its monopoly on fiat for the purpose of extracting seigniorage -- such an extension is possible, but beside the point here). But ultimately, my response is this: what phenomenon might be better understood, in the context of the present discussion, by distinguishing money from debt? You tell me how what I have done here is in any way misleading because of my failure to take the medium of exchange role of money more seriously.

It is interesting to note that in making no distinction between money and debt here, the Fed finds itself in a perpetual liquidity trap.  That is, any swap of money and bonds is completely irrelevant for anything real or nominal. The two objects are perfect substitutes in the model. In fact, I think this describes the current situation along one dimension rather well. In particular, interest-bearing reserves are virtually indistinguishable from government treasuries as far as banks are concerned (so swaps of treasuries for interest-bearing reserves should have little, if any, consequences).

Along the same vein, if you want, think of the case in which R = 1 (zero nominal interest rate). This is the scenario that most people associate with a liquidity trap, but as the preceding discussion makes clear, one does not need to hit the zero lower bound to speak of liquidity traps.

1. David,

I'm not up on the various monetary models, but I do find this to be a cogent model for thinking of how an intermediary divides it's assets.

The main insight I see is that price level changes are the transmission of information from private view to public view, like stock prices. The primary difference is that the price level changes reflect information about many firms/households, whereas stock price changes are one firm.

A follow-up question, and depending on the answer I have more to add. Can one think of inflation as a discount factor? Then when prices are increasing that means the rate of return is negative?

2. Prof J: Changes in a stock price index reflect information about many firms. Inflation as a discount factor? Not sure about that. In answer to your last question: let v(t) denote the price of cash (the inverse of the price-level). Then the real rate of return on non-interest-bearing cash is v(t+1)/v(t), which is the inverse of the inflation rate. So yes, with positive inflation, the real rate of return on non-interest-bearing money is negative.

3. David,

Yes, changes in the price index (like S&P 500) are about many firms at once. I was referring to an individual firm's stock price. But that's all fine, I see where you're going.

Now, the reason I would like to think of inflation as a discount factor is that I can bring in some tools from the asset pricing literature.

Please correct my thinking on this issue if I'm wrong, but here goes. Your model seems to base the intermediary's decision to lend or hold government debt based on future productivity of capital. If the intermediary receives a news shock that is disfavorable regarding future capital productivity, said intermediary will shift holdings away from loans to private business and into government assets. To a corporate finance person, this would be interpreted as a cash flow shock. For example, some bad news could indicate our groovy investments in real estate are going to generate about half the rent we thought, and we'd want to trim investment if at all possible.

The other issue could be a discount rate shock, though. I believe these are separate but correlated issues. My rental stream may receive to revision, but due to competition for financial capital my required return may go up. In such a case, capital may shift away from current projects into other ones. And, of course, vice versa.

So the reason I want to think of inflation as a discount factor is that news shocks regarding inflation could affect intermediaries' holdings of loans & government assets.

Now, was that last point clear in your model and I missed it? I have a habit of running into trees while I'm looking for the forest. If it isn't coming from your model, then maybe I'm wrong, or it's irrelevant to this situation.

4. OK, let's get to work. (Spits on palms of hands, rubs them together).

Let's simplify the model initially, by assuming there's no money/debt or government/central bank. The only asset is real capital k. The level of desired savings is constant and exogenous, and if k is the only asset, market-clearing requires desired savings must equal desired investment in k. And the real rate of interest adjusts to make this happen. Shocks to w (news) do not affect equilibrium investment, but do affect the real rate of interest.

OK, that initial simplified version makes logical sense. Given the time-path of w, this model determines a unique time-path for k and the real interest rate.

Now, lets introduce a consolidated government/central bank. Call it "govt". The govt prints an asset called M, and it has a price 1/P in terms of k. M and k are perfect substitutes in the eyes of savers (that's the big assumption). With no loss of generality, assume M pays zero nominal interest. So this requires the expected rate of inflation on M to equal the real interest rate, which in turn equals the expected marginal product of k.

Now, we hit upon an immediate problem. To make it clear what the problem is, consider the thought experiment where we introduce govt into the model in real time. In other words, we start out in a world with no govt, that is exactly like my simplified version. We are in equilibrium, and there is an expected equilibrium time-path, conditional on w. Then at time t someone unexpectedly invents govt, and M (which gets helicoptered in).

Since at time t the economy is in equilibrium, there is zero demand for M (or M/P). Desired savings equals desired investment everywhere along the foreseen equilibrium time-path. If their expectations of the time path of k don't change, there is zero demand for M, at time t and at all future periods.

As theorists, we could create an equilibrium demand for M/P, and make it as big as we like, by changing investment at time t, and changing people's expectations of the whole time path of k in an appropriate way. If we lower k by just the right amount at all periods, we can "make room" for any given amount of M/P in people's portfolios.

But the cost of introducing M into the model in this way is that we lose the uniqueness of the equilibrium time-path. There is an infinite number of equilibrium time-paths. And there is nothing to pick between them. That means we cannot meaningfully make any statements about comparative statics. "What is the effect of a permanent doubling in M?". Answer: anything can happen. There is one equilibrium in which P doubles in all periods, and everything else stays the same. And a host of other equilibria. Anything can happen to P today.

M gets introduced into this model as a pure bubble asset, or Ponzi asset.

To be continued...

5. Prof J: I like the way you summed things up in your third paragraph. Now, let's see how to think about a discount rate shock in this model. First off, in this model, the government is assumed to control both the nominal interest rate and the *long-run* expected inflation rate. Any shock to either of these will act as a discount shock. In the model, as I have written it above, a news shock has a temporary impact on *expected* inflation (if the news shock is i.i.d.). So it does impact on the discount factor (although the impact on the expected MPK is dominant, I think). I'm not sure any of this helps. Let me know.

Nick: Ah yes, it is a delicious model, isn't it? Yes, you are right, there is an indeterminacy in this model. But then, this is not surprising, is it? It is a model that supports an asset bubble...a huge liquidity premium (defined as market value over fundamental value). Isn't valued fiat money all about a self-fulfilling prophesy? And while there are many possible outcomes, I have focused on stationary equilibria (and even here, there are two possible outcomes). So, I'm not sure whether you meant your remarks to be a criticism or a compliment!

6. OK, let's change the model so it's an OLG model. Assume every old agent must consume y or die, and that the marginal utility of any consumption above y is zero. That pins down savings by the young, and k.

Again, assume an initial equilibrium with no govt of M. Suppose it's dynamically inefficient. That creates a demand for M. There are now only two stationary equilibria: one with P finite, and one with P infinite (which is the same as the initial equilibrium). Let's restrict attention to the stationary equilibrium with finite P. So we can meaningfully do comparative statics.

A permanent doubling of M by helicopter (to existing holders of M, so there's no distribution effects), and so the whole time-path of M doubles, causes P to double at all points along the time path, and k to stay the same. QTM and neutrality holds.

Now suppose M increases by an OMO. The govt uses extra M to buy some k. What happens?

The answer depends on what the govt is expected to do with the k it buys.

If the govt is expected to do a reverse OMO at some future period, so it sells all the extra k it bought, including the re-invested returns on that k, then there is no effect either on P or on any real variable. The govt is just acting as banker. This is your case David.

If we assume the OMO gets reversed in 1 period, for simplicity, then M increases by dM today, but is expected to decrease by (1+r)dM next period (where r is the real rate of interest), then the OMO has no effect, either real or nominal.

A Quantity theorist would split this reversed OMO experiment into 2 parts:
1. The increase in current M causes current P to increase.
2. The decrease in expected future M causes expected future P to decrease, which causes current P to decrease.

And the two effects exactly cancel out in this case. Why do they *exactly* cancel out? Because by assumption M and k are perfect substitutes, so yield the same real return in equilibrium. And because the govt uses *all* the proceeds from the current OMO (including the return on k) for the future reverse OMO.

Relax either of those two assumptions, and the future reverse OMO will not exactly cancel the current OMO.

For example, if the govt spends the returns on its k for something the govt wants, that has no effect on the private MU of consumption (e.g. pyramids), it will not be able to do the future reverse OMO in a big enough amount to fully offset the effects of the current OMO.

And if all the future returns on its k are dedicated to building pyramids, forever, it cannot do a future reverse OMO at all. In that case, a current OMO where the returns are spent on pyramids forever, is equivalent to a helicopter drop plus a tax-financed permanent increase in G. (Equivalently, a permanent helicopter increase in M plus torch some k.)

And that second case matches the implicit assumption of Quantity Theorists. They assume that the annual interest from the Fed's assets get handed over to the government, and spent on pyramids.

7. David: I was writing my second comment before reading your reply to my first. (Just so it's clear why I was ignoring you!)

8. Nick:

Beautiful.

Let me correct one minor thing (does not affect any of your conclusions). In fact, I was thinking of OLG to begin with. If capital is the only asset, then the young save k = y, and they consume zf(y) when old. If zf'(y)<1, then there is a dynamic inefficiency (and a role for government debt). In fact, the dynamic inefficiency is present even if E[zf'(y)|w] for any news state w (a considerably weaker condition).

So what do we conclude from this? In my earlier post, I suggested that the Fed's MBS asset purchase need not have price-level effects because the Fed was purchasing a real interest-bearing asset. But I should have been explicit about what use the earnings are being put to. In part, they are used to pay interest on reserves. But a good piece of change is being remitted to the Treasury. The theoretical effect of the purchase then depends on what the Treasury plans to do with the money (e.g., destroy it, pay off debt, or increase spending, etc.). More importantly, it depends on what the market *believes* will transpire in the future.

This is all consistent with more generalized versions of the QTM. Of course, I like my model better for a number of reasons:

[1] It derives, rather than assumes, a demand for government money/debt.

[2] The implication of [1] is to point out an inherent fragility in the equilibrium that supports valued fiat money.

[3] There is a welfare-enhancing role for such debt.

[4] The model let's us think clearly about what would generate what you (and others) have labelled an exogenous increase in the demand for money.

[5] Money is not necessarily neutral (although one might quibble about redistributive effects)

[6] I like the model predictions about M1 and the money multiplier--seems consistent with the evidence.

[7] The model's predictions are broadly consistent with the evidence...even though there are NO sticky prices! :)

9. David:

I thought you might have an OLG model at the back of your mind!

1. What that derives is a demand, not for a medium of exchange, but for a Pay As You Go unfunded government-sponsored pension plan. An unbacked positive net wealth asset. There is nothing in that model that says that "money" must function as a medium of exchange, so that "goods buy money, and money buys goods, but goods do not buy goods" (Clower).

I can derive a demand for sardine-flavoured ice cream, if I price it low enough. What's astounding about money is that people still want to hold (some) of it even at Zimbabwean rates of inflation. That makes sense if transactions costs of barter mean that people will use a medium of exchange, and will hold (some) of it even when it is massively rate of return dominated by other assets.

2. There is indeed an inherent fragility in the equilibrium where fiat (I prefer the word "fiduciary") money has value. If people think it will be worthless in future, then it is worthless today. Von Mises attacked (and I think solved) this problem (The "Hahn problem") with his "Regression theory of money". Fiat/fiduciary money does not appear ex nihilo in real time. It evolves out of convertible money. When we have a model with two equilibria, history matters. History provides a Schelling focal point to coordinate expectations. Start out with a redeemable (convertible) money, get people used to the equilibrium in which money has value, then suspend redeemability, and the money keeps flying under its own power. Languages work like this. There is no fundamental reason why "dog" means dog. It just does, because of history.

But that dual equilibrium problem is inherent in all models of fiat/fiduciary money. And it's quite distinct from the question of whether the economy is or is not dynamically inefficient, which depends on the values of fundamental parameters.

In any case, presumably historically some economies have been dynamically efficient, and some inefficient. But all (except the most primitive) have been monetary exchange economies. Why? Because it's too damn hard to do the shopping if you don't hold, om average, a positive stock of the medium of exchange. And barter makes shopping even harder. That's why there's a demand for money. Even in Zimbabwe.

3. Plus, if you want to explain a welfare-enhancing role for government *debt*, that's easy. "There's a war on", plus distortionary taxes and the tax-smoothing motive, can motivate government debt. (And why would you want to assume that everything the government does is welfare-enhancing? You some kind of pinko?)

4567. OK. But is this the *only* sort of model that can do that?

I need to write a post on "Is money net wealth?". That question (and an old 1960's literature on that question) bears tangentially on the sort of model you are using. Like Gurley and Shaw, you assume that money is net wealth if and only if it is outside (unbacked) as opposed to inside (backed) money. Pesek and Saving showed that was wrong. The key distinction is between monopoly (net wealth) and competitive (not net wealth) money.

Must sober up. Keep posting.

10. Nick:

While I had an OLG model in mind, the condition I wrote down holds more generally in New Monetarist models with infinitely-lived agents. So do not get hung up on the common mistake of interpreting OLG too literally. Now, on to your points.

[1]The PAYG statement suggests that you are interpreting the overlapping generations structure too literally. The model is one in which people need assets to pay for goods (their credit is no good, because they are anonymous). The question is then: which set of assets might be used to purchase goods? In my model, both private and government assets serve as a payment instrument. I'm not sure I know what PAYG has to do with anything.

Also, note that any store of value may be held at extremely low rates of return. There is nothing that says the real rate of interest must be positive.

[2] That's nice: thank's for pointing it out to me.

[3] lol

Nick, you have not yet addressed this question I posed in my post:

"But ultimately, my response is this: what phenomenon might be better understood, in the context of the present discussion, by distinguishing money from debt? You tell me how what I have done here is in any way misleading because of my failure to take the medium of exchange role of money more seriously."

That is, I have presented a model where bad news leads to a recession. Investment collapses and there is a flight to quality. [If you were watching data pouring out of this economy, you would have labeled it a shock that generates and excess demand for money.] As investment is collapsing in my model, bank balance sheets are contracting, the money multiplier declines, and the price-level falls. Tell me what part of this story you find so unconvincing. Is it because there are no sticky prices?

11. Damn! It ate my comment, before I could post it!

Trying again.

Slightly off-topic: "So do not get hung up on the common mistake of interpreting OLG too literally." I have been hung up on that point for 30 years. I can see that OLG must be taken very metaphorically as a model of money (less metaphorically as a model of pensions). But which bits of the metaphor can be applied, and which not?

Define "velocity" literally, for a minute, as the number of times per year an asset changes hands. And not as PY/M. As we look across the spectrum of assets we see a positive correlation between an asset's velocity and its liquidity, which have a negative correlation with its rate of return. Money is at one extreme end of the spectrum. In fact, when all the other assets change hands, they change hands for money.

So any model of money that doesn't have this feature, and has bonds being barter for goods, and money and bonds having the same velocity, seems to me to miss something important about money.

Back on topic: "what phenomenon might be better understood, in the context of the present discussion, by distinguishing money from debt?"

My sense is that it is much harder than normal to sell things (both outputs and inputs), and much easier than normal to buy things. That looks like generalised excess supply. And my sense is that people would buy more outputs if they could sell more inputs, and firms would buy more inputs if they could sell more outputs. The incentive for direct barter "looks" much stronger than normal.

Both those "observations" only make sense in a monetary exchange economy. Otherwise people would barter their inputs for firms' outputs. There must be an excess demand for the medium of exchange in at least some of the n markets, to match the excess supplies of goods in those markets.

Yep, that's not hard StatsCan data. StatsCan measures Ps and Qs, not excess supplies. But it does fit with StatsCan data on unemployment.

The "observation" of sticky prices helps me make sense of the story.

12. Nick:

I don't want to get too hung up on OLG, but since you have been for the past 30 years, let's see if we might not make some progress.

First, let me try to clear some things up that may or may not be important; but may be of interest nevertheless.

Consider a standard Wicksellian triangle model. We can extend this model to a Wicksellian circle with N nodes (each representing a type of agent). This model is a useful way to explain the need for a circulating medium (we need more assumptions, of course, to rule out Arrow-Debreu securities markets, etc.). Now let N go to infinity. Viola, you have an OLG model.

Let me put it another way. One can assume that everyone lives forever in an OLG model. We can reinterpret the meetings of "young" and "old" as meetings of two types of agents at remote locations, never to meet again. In short, I can get "velocity" to be as high as I want -- I do not have to think of OLG people as trading at 30-year intervals.

Any thoughts?

Also, I do not think you answered my question very well. I gave you a theory of recessions. The theory generated predictions that I think are broadly consistent with some key facts. I asked what part of my explanation depending on me making a distinction between government money and debt?

You've been a big help to me so far -- this is no time for you to get lazy!

13. David,

Going back to your original question as to why the sharp increase in the monetary base has not led to a porpotional increase in the price level, I would reiterate the importance of the money multiplier and velocity (i.e. real money demand).  Yes, the monetary base has more than doubled, but the money multiplier has fallen by a similar amount. On top of that velocity has fallen too. (See here for a graph and more on this point for the 2008- 2009 period.)

In terms of a formal framework in which to think about this, I like to fall back on the simple equation of exchange identity, expanded to include the money multiplier. If we set M=Bm, where M is the money supply, B is the monetary base, and V is velocity, then the equation of exchange becomes: BmV=PY. With this in hand one can see how large increases in B can be offset by drops in m and V. Bruce Bartlett recently brought up a similar point as yours on this issue.  Here is how I responded to him.

BTW, impressive use of equations in your post.

14. David: on OLG: Yes, that sort of OLG variant makes more sense to me. But to have both money and bonds, we need some sort of high-frequency circular structure, for money, and superimposed on it we need some sort of longer wave low-frequency structure, for bonds.

On a daily basis people switch from being buyers to sellers of goods+bonds for money. On an annual basis, people switch from accumulating bonds to decumulating bonds.

So if you zoom in to the daily picture you see a model of monetary exchange, and if you zoom out to the annual picture you see a model of borrowing and lending in bonds.

I hope that makes sense (I wish I could explain this more clearly).

"I asked what part of my explanation depending on me making a distinction between government money and debt?"

I don't think any part of your explanation depends on a distinction between money and bonds (in other words, I can't see any internal inconsistency in your explanation). Some facts can be explained without talking about money at all. I expect that what i was doing is to say there are other key "facts" (only they are not really hard facts, just my sense of how the world looks) that can't be explained without distinguishing money from all other assets.

Thanks for saying I'm a help. And reading your stuff is a great help to me. Because I'm just so out of it, as far as much of the modern literature is concerned. Reading and arguing with you and Steve Williamson is how I'm trying to keep up.

15. By the way, here is my own slightly pathetic attempt to integrate money into the ISLM model formally: http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/05/the-is-curve.html

During the trading day, workers are randomly divided into "early shoppers" who need to have money to buy things, and "late shoppers", who can earn money from the early shoppers. It's sort of a high-frequency trading circle, just split into two halves, so you can't sell and buy at the same time.

16. Nick,

I agree that sticky prices help make sense of the observation of generalized excess supply, but I don't believe that you need monetary exchange. What you need is the possibility to save an unlimited fraction of your income.

Prices (assuming they are sticky) are almost as sticky in terms of bonds as they are in terms of money. If we lived in your bling economy, workers would require part of their pay in the form of bonds. (That is, bonds would be offered on eBazon, and workers would trade part of their labor for bonds.) If there were a shortage of bonds, and workers couldn't get all the bonds they wanted, that would be a constraint on individual saving. There is no "paradox of thrift" in the bling economy, only because the institutional arrangements disallow thrift in the case where the paradox would apply. But as long as you allow people unlimited access to bonds (and assuming the interest rates are constrained to be nonnegative), an excessive preference for owning those bonds will lead to unemployment.

17. Andy: I just don't get it. In a barter economy, with an excess demand for bonds, this is what happens: the unemployed worker goes to the firm and says "I will work for bonds", and the firm says "No, we don't have any". So the worker then says "OK, second best, I will work for the widgets you produce, because widgets aren't as good as bonds, but a lot better than nothing".

Does an excess demand for rent-controlled rental apartments cause an excess supply of everything else, and a general glut? No. (Though it does harm labour mobility, true).

18. Nick,

If you tell someone that there are no savings vehicles available, you're preventing them from saving. Of course there is no paradox of thrift when there is an absolute limitation on how thrifty an individual can be. You could do the same thing in a monetary exchange economy by putting a statutory limit on personal saving.

I believe it's logically impossible to have a barter economy with unconstrained nominal saving. In a monetary economy with unconstrained nominal saving (and sticky wages), you blame the unemployment on the money and I blame it on the saving.

The critical feature, though, is not that wages are sticky in terms of the medium of exchange but that they are sticky in terms of the saving asset. Suppose, for example, you have a barter economy where the saving asset is corporate equity, and suppose that convention demands that workers' pay be proportional to the value of a share of stock (or suppose workers are paid a fixed number of shares of stock). Then you will get a paradox of thrift, because saving will lead to increases in the price of stock, and workers will require higher wages, which firms will be unwilling to pay. You can say that it's irrational for workers to demand higher wages under those conditions, but it's equally irrational (isn't it?) for them to demand fixed money wages in a monetary exchange economy.

19. David Beckworth: Thanks...I am trying to find a better way to write equations in html, but I suppose that this does look OK. And yes, I agree with you that velocity (or the money multiplier) is key here. No need for me to write down simple identities, however. I like the little model here, which explains *why* the money multiplier is behaving the way it is. Thanks for the links, although I'm not sure how much I agree with what Bruce Bartlett says!

Nick and Andy, I'm afraid that I'm not following the argument, but please feel free to duke it out here! :)

20. Turns out the question of what I mean by "shares of stock" in my last example is more complicated than I thought, and I'm not sure under what conditions the paradox holds.

If we're talking about a generic saving asset, though, I think it depends on whether all prices are equally sticky. If all prices are equally sticky, then increased attempts to save will result in a shortage of the saving asset and thus prevent individuals from saving, thereby "short-circuiting" the paradox of thrift by limiting the opportunity for thrift. If the wage is sticky in terms of the saving asset and other prices are less sticky, then saving will push up the real wage and result in unemployment, thus a (potential) paradox of thrift.

Note also that in a monetary economy where workers are paid in money but paid a wage that is in fixed proportion to the price of a non-monetary saving asset (e.g. non-monetary gold in a fiat money economy), there will be a (potential) paradox of thrift that cannot be solved by increasing the supply of money.