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

Monday, October 20, 2014

What's holding back female employment?

Almost four years ago, I asked whether the U.S. was in for a labor market slump similar to the slump experience in Canada during the 1990's. Evidently, the answer turned out to be yes.

How is the U.S. faring relative to Canada back then? American prime-age males seem to be tracking their Canadian counterparts, both in terms of employment-to-population ratios and in labor force participation rates. American females, on the other hand, appear to be lagging behind their Canadian counterparts. Let me show you some data.

Let's begin by looking at the employment ratio for prime-age males:

As you can see, the sharp drop and subsequent recovery dynamic for prime-age males is remarkably similar across these two countries and time periods. (The initial E-P ratio was about 87% for both countries; see here).

Here is what their labor force participation rates look like:

Again, the recovery dynamic looks almost identical (The initial part rate for Canada was 93%, for the US about 91%; see here).

Alright, now let's take a look at the same statistics for prime-age females. First, the employment ratios:

These dynamics look quite a bit different. The main effect of the recession in Canada was to slow down the growth rate in the employment ratio. In the U.S., the effect has been to reduce the employment ratio, with only a very weak sign of recovering in the past year.

Here is what the labor force participation rate dynamics look like:

Again, two very different recovery dynamics.

A colleague of mine suggested that state-level layoffs in education and government may explain a good part of the lackluster recovery dynamic for U.S. females. This is certainly worth looking into. However, if we take a look at the following diagram, we see that the discrepancy appears to have happened much earlier -- around 1997, in fact.

It seems unlikely to me that the divergence between Canadian and American prime-age females is driven by cyclical considerations (although, a small part of the recent gap may be). Work incentives are likely to have changed, although what these changes were, I do not yet know. In any case, I doubt that monetary policy is a tool that can be used to close this gap. I can think of plenty fiscal interventions that might help, however.

Addendum Oct. 22, 2014

My colleague, Maria Canon, points me to the following paper by Sharon Cohany and Emy Sok Trends in labor force participation of married mothers of infants, as well as this interesting set of slides by Jennifer Hunt: Female labor force participation: slack and reform.

And here's a real doozy "Universal Child Care, Maternal Labor Supply, and Family Well-Being" by Michael Baker, Jonathan Gruber, and Kevin Milligan (JPE 2008). From the abstract:
We analyze the introduction of highly subsidized, universally accessible child care in Quebec, addressing the impact on child care utilization, maternal labor supply, and family well-being. We find strong evidence of a shift into new child care use, although some crowding out of existing arrangements is evident. Maternal labor supply increases significantly. Finally, the evidence suggests that children are worse off by measures ranging from aggression to motor and social skills to illness. We also uncover evidence that the new child care program led to more hostile, less consistent parenting, worse parental health, and lower-quality parental relationships.

Monday, September 8, 2014

Who's Afraid of Deflation?

Everyone knows that deflation is bad. Bad, bad, bad. Why is it bad? Well, we learned it in school. We learned it from the pundits on the news. The Great Depression. Japan. What, are you crazy? It's bad. Here, let Ed Castranova explain it to you (Wildcat Currency, pp.160-61):

Deflation means that all prices are falling and the currency is gaining in value. Why is this a disaster? ... If you hold paper money and see that it is actually gaining in value, it may occur to you that you can increase your purchasing power--make a profit--by not spending it...But if many people hold on to their money, this can dramatically reduce real economic activity and growth...

In this post, I want to report some data that may lead people to question this common narrative. Note, I am not saying that there is no element of truth in the interpretation (maybe there is, maybe there isn't). And I do not want to question the likely bad effects that come about owing to a large unexpected deflation (or inflation).  What I want to question is whether a period of prolonged moderate (and presumably expected) deflation is necessarily associated with periods of depressed economic activity. Most people certainly seem to think so. But why?

The first example I want to show you is for the postbellum United States (source):

Following the end of the U.S. civil war, the price-level (GDP deflator) fell steadily for 35 years. In 1900, it was close to 50% of its 1865 value. In the meantime, real per capita GDP grew by 85%. That's an average annual growth rate of about 1.8% in real per capita income. The average annual rate of deflation was about 2%. I wonder how many people are aware of this "disaster?"

O.K., well maybe that was just long ago. Sure. Let's take a look at some more recent data from the United States, the United Kingdom, and Japan. The sample period begins in 2009 (the trough of the Great Recession) and ends in late 2013. Here is what the price level dynamic looks like since 2009:

Over this five year period, the price level is up about 7% in the United States and about 11% in the United Kingdom. As for Japan, well, we all know about the Japanese deflation problem. Over the same period of time, the price level in Japan fell by almost 7%.

Now, I want you to try to guess what the recovery dynamic--measured in real per capita GDP--looks like for each of these countries. Surely, the U.K. must be performing relatively well, Japan relatively poorly, and the U.S. somewhere in the middle?

You would be correct in supposing that the U.S. is somewhere in the middle:

But you would have mixed up the U.K. with Japan. Since the trough of the past recession, Japanese real per capita GDP is up 15% (as of the end of 2013)--roughly 3% annual growth rate. Is deflation really so bad? Maybe the Japanese would like the U.K. style inflation instead? I don't get it.

I have some more evidence to contradict the notion of deflation discouraging spending (transactions). The evidence pertains to Bitcoin and the data is available here: Blockchain.

Many people are aware of the massive increase in the purchasing power of Bitcoin over the past couple of years (i.e., a massive deflationary episode). As is well-known, the protocol is designed such that the total supply of bitcoins will never exceed 21M units. In the meantime, this virtual currency and payment system continues to see its popularity and use grow.

One might think that given the prospect of continued long run deflation--i.e, price appreciation (it's hard to believe that holders of bitcoin are thinking anything else)--that people would generally be induced to hoard and not spend their bitcoins. And yet, available data seems to suggest that this may not be the case:

Maybe deflation is not so bad after all?  Let's hope so, because we may all have to start getting used to the idea!

Additional readings:
[1] Good vs. Bad Deflation: Lessons from the Gold Standard Era (Michael Bordo and Angela Redish).

[2] Deflation and Depression: Is There an Empirical Link? (Andy Atkeson and Pat Kehoe).

[3] The Postbellum Deflation and its Lessons for Today (David Beckworth).

Friday, July 25, 2014

Debt: The First 5000 Years

Ah, the airport bookstore. As monetary theorist and history buff, I could not resist this tantalizing title: Debt: The First 5000 Years. The book is authored by anthropologist David Graeber, a leading figure in the Occupy Wall Street movement. But what grabbed me was the summary on the back cover, which states (among other things) that every economics textbook is wrong in the way it explains the emergence of money, which goes something like this: "Once upon a time, there was barter. It was difficult. So people invented money." [p28].

I think we (economists) have to score one for the anthropologists here. I remember being taught that story and it took me some time to figure out it was wrong. What makes barter difficult? We are taught that the difficulty stems from a "lack of coincidence of wants." Consider, for example, an island populated by three people, Adam, Betty and Charlie. Adam wants breakfast, Betty wants lunch, Charlie wants dinner. Adam can deliver dinner, Betty can deliver breakfast, and Charlie can deliver lunch. There are no bilateral gains to trade (no voluntary trade would occur between any arbitrary pairing of individuals). And yet, there are clearly multilateral gains to trade.

The solution, we are told, is to introduce a monetary object and endow it to Adam, who may then purchase his breakfast from Betty with cash. Betty then uses her money to buy lunch from Charlie. Charlie then uses his money to buy dinner from Adam, and so on.

As anthropologists have pointed out for a long time, there is really little evidence of trade taking this form in primitive communities (see: Famous Myths of Fiat Money, by Dror Goldberg). Instead, these societies operated as "gift giving" economies, or informal credit systems. The principle should be familiar to all of us: it is reflected in the way we trade favors with friends, family, and other members of social networks to which we belong.

What then, explains monetary exchange (really, the coexistence of money and credit)? According to Kiyotaki and Moore, Evil is the Root of All Money. "Evil" here is interpreted as the existence of untrustworthy (noncooperative) people. Untrustworthy individuals readily accept gifts from the community, but cannot be trusted to fulfill their implicit obligation to reciprocate in-kind when an opportunity to do so arises. However, we know from game theory that a system of "cooperative" exchange might still be sustained if untrustworthy people can be compelled to behave properly, say, by the threat of punishment for noncompliant behavior (e.g., ostracism from the community).

The punishment/reward system that implicitly exists in gift-giving societies requires (to the extent that some community members are untrustworthy) a communal monitoring of individual behavior. In small communities, "everybody knows everything about everyone" and so this is arguably why "communistic" societies can be sustained in small groups. It also suggests why the arrangement breaks down for larger groups. The virtual communal data bank -- a distributed network of computer brains -- is simply not capable of recording all the information necessary to support an informal credit system in a large population. In a large population, people can remain anonymous. We necessarily become strangers to most people. And its tough to trust a stranger (a person you are not likely ever to meet again).

Nevertheless, multilateral gains to trade may still exist even among strangers. And if credit is difficult, or impossible, then the solution is money (see: The Technological Role of Fiat Money, by Narayana Kocherlakota). According to this theory, money serves as a substitute for the missing communal memory. Contributions to society are now measured not by virtual credits in the collective mind of the community; instead, they are recorded by money balances (this assumes, of course, that money, like virtual credit, is difficult to counterfeit/steal).

So, in a nutshell, economic theory suggests that we use informal credit arrangements to govern exchange among people we know (family, friends, colleagues, etc.) and we use money to facilitate exchange with "strangers." The emergence of money then seems tied to the emergence of strangers. An obvious explanation for this is population growth (and the associated rise of large urban areas).

One thing I learned from Graeber is that the relative importance of money and credit seems to have waxed and waned over time. Money (in particular, coinage) emerged around 800BC and remained significant until about 600AD, an era associated with many great empires, and the associated need to pay transient professional armies. With the collapse of the great empires, new states emerged, increasingly under the regulation of religious authorities. Coinage declined in importance, with credit systems taking over (600AD-1450AD). This latter observation is consistent with the general decline of urban areas in western Europe, but Graeber points to many other factors as well. Monetary exchange waxes once again with the age of the "great capitalist empires" (1450-1971AD).

My comments above only scratch the surface of the book's much broader thesis concerning the moral nature of debt. The presentation is not as clean as it could be, the analysis is sloppy in several places, and the conclusion is rather weak but, heck, it's still a very interesting read. If nothing else, it encouraged me to interpret various aspects of history in ways that I am not accustomed to.

Alas, every gain comes at a price (beyond the $22 cash I paid for his book). His opening chapter, in particular, is so annoying that it almost led me to abort the enterprise. In the book, and in the many interviews he gives, he relays the following story (source):
And one of the things that really fascinated me was the moral power of the idea of debt. I would tell stories to people, very sympathetic people, liberal lawyers, well-meaning do-gooder types, and you’d tell these stories about horrible things. You know, in Madagascar, for example, the IMF came in with these policies, you have to cut the budgets because, god knows, we can’t reduce the interest payments you owe to Citibank, they owed all this money. And they had to do things like get rid of mosquito eradication programs, as a result that malaria returned to parts of the country where it had been wiped out for a hundred years and tens of thousands of people died and you had dead babies being buried and weeping mothers. I was there, I saw this sort of thing. You described this to people and the reaction would be, well, that’s terrible, but surely people have to pay their debts. You’re not suggesting they cancel it or default, that would be outrageous. And one of the things that really fascinated me was the moral power of the idea of debt.
I'm not completely sure, but if I was to relay this story to the average person I know, I would hardly expect them to say "well, that's terrible, but surely people have to pay their debts!" I'm pretty sure that most of the people I know would have replied "that's $^%& outrageous!" But then, maybe I don't know too many "sympathetic" people, liberal lawyers and well-meaning do-gooder types.

Moreover, I'm pretty sure that a significant majority of the people I know would have questioned the claim that the IMF kills African babies. After all, we are not speaking here of a paragon of good government.
Since Madagascar gained independence from France in 1960, the island's political transitions have been marked by numerous popular protests, several disputed elections, an impeachment, two military coups and one assassination. The island's recurrent political crises are often prolonged, with detrimental effects on the local economy, international relations and Malagasy living standards. (source)
Of course, malaria was for a long time a big problem on the African continent (see here) and elsewhere. But the disease was practically wiped out with the use of the pesticide DDT (see here). The use of DDT was then banned, owing to pressure from "well-meaning do-gooder" environmental groups. [Evidently, the ban was primarily for agricultural use, and only sometimes in vector control]. Now, according to this source:
In the 1980’s Madagascar stopped using DDT and immediately had an epidemic of malaria, resulting in the death of more than 100,000 people.
Hmm. And according to this source:
A strong malaria epidemic with a high mortality rate occurred on the Madagascar Highlands in 1986-88. Vector control and free access to antimalaria drugs controlled the disease.
This latter source also mentions the lack of immunity and a shortage of medicaments as factors contributing to the mortality rate. Is Graeber suggesting that the shortage of medicaments was the consequence of IMF imposed austerity measures on Madagascar's government and the desire to service Citibank debt? It seems an unlikely story (although, it's not easy to find details). According to this data from the World Malaria Report, almost all the resources for fighting malaria in Madagascar originates from international aid organizations, like USAID and The Global Fund. Did the IMF prevent these agencies from doing their good work?

Finally, let me point readers to Ken Rogoff's defense of IMF policies here. See also the article here, by Masood Ahmed.

Make no mistake, the malaria episode described by Graeber is a tragic story. People were dying and somewhere the resources existed that could have mitigated the losses (a continued program of DDT spraying would have prevented it altogether). Among other things, the government of Madagascar could have reallocated resources away from some expenditure (say, military, which is 1% of GDP according to CIA Factbook) toward medicaments. That it evidently chose not to is revealing. Does Graeber truly believe that a "debt jubilee" for governments of this nature would have prevented the episode in question? (Note: I am not against debt jubilees.)

Graeber has many useful and interesting things to say in his book. I personally find it annoying that a scholar and writer of such high caliber has to resort to stories like this to sell his ideas. But maybe that's just me. In any case, my recommendation is to read the book and filter out as much of the noise as you can. 

Wednesday, June 25, 2014

Excess reserves and inflation risk: A model

Note: The following is an edited version of my original post. Thanks to Nick Edmonds for pointing out an inconsistency in my earlier analysis. Nick's comment forced me to think through the properties of my model more carefully. In light of his observation, I have modified the original model to include capital investment. My earlier conclusions remain unchanged. 

I should have known better than to reason from accounting identities. But that's basically what I did in my last post and Nick Rowe called me out on it here. So I decided to go back and think through the exercise I had in mind using a simple model economy.

Consider a simple OLG model, with 2-period-lived agents. The young are endowed with output, y. Let N denote the number of young agents (normalize N=1). The young care only about consumption when they are old (hence, they save all their income y when young). Agents are risk-averse, with expected utility function E[u(c)]. There is a storage technology. If a young agent saves k units of output when young, he gets x*f(k) units of output in the next period, where x is a productivity parameter and f(.) is an increasing and strictly concave function (there are diminishing returns to capital accumulation). Assume that capital depreciates fully after it is used in production.

If x*f'(y) > 1, the economy is dynamically efficient. If x*f'(y) < 1, the economy is dynamically inefficient (and there is a welfare-enhancing role for government debt).

Now, imagine that there are two such economies, each in a separate location. Moreover, suppose that a known fraction 0 < s < 1 of young agents from each location migrate to the "foreign" location. The identity of who migrates is not known beforehand, so there is idiosyncratic risk, but no aggregate risk.

Next, assume that there are two other assets, money and bonds, both issued by the government supply (and endowed to the initial old). Let M be the supply of money, and let B denote the supply of bonds. Let D denote the total supply of nominal government debt:

[1] D = M + B

Money is a perpetuity that pays zero nominal interest. Bonds are one-period risk-free claims to money. (Once the bonds pay off, the government just re-issues a new bond offering B to suck cash back out of the system.) Assume that the government keeps D constant maintains a fixed bond/money ratio z = B/M, so that [1] can be written as:

[2] D = (1+z)*M

In what follows, I will keep D constant throughout and consider the effect of changing z (once and for all). Note, I am comparing steady-states here. Also, since D and M remain constant over time, and since there is no real growth in this economy, I anticipate that the steady state inflation rate will be equal to zero.

Let R denote the gross nominal interest rate (also the real interest rate, since inflation is zero). Assume that the government finances the carrying cost of its interest-bearing debt with a lump-sum tax,

[3] T = (R-1)*B

The difference between money and bonds is that bonds (or intermediated claims to bonds) cannot be transported across locations. Only money is transportable. The effect of this assumption is to impose a cash-in-advance constraint (CIA) on the young agents who move across locations. (Hence, we can interpret the relocation shock as an idiosyncratic liquidity shock).

Young agents are confronted with a portfolio allocation problem. Let P denote the price level. Since the young do not consume, they save their entire nominal income, P*y. Savings can be allocated to money, bonds, or capital,

[4] P*y = M + B + P*k

There is a trade off here: money is more liquid, but bonds and capital (generally) pay a higher return. The portfolio choice must be made before the young realize their liquidity shock.

Because there is idiosyncratic liquidity risk, the young can be made better off by pooling arrangement that we can interpret as a bank. The bank issues interest-bearing liabilities, redeemable for cash on demand. It uses these liabilities to finance its assets, M+B+P*k. Interest is  only paid on bank liabilities that are left to mature into the next period. (The demandable nature of the debt can be motivated by assuming that the idiosyncratic shock is private information. It is straightforward to show that truth-telling here in incentive-compatible.)

Let me describe how things work here. Consider one of the locations. It will consist of two types of old agents: domestics and foreigners. The old foreigners use cash to buy output from the domestic young agents. The old domestics use banknotes to purchase output from the young domestics (the portion of the banknotes that turn into cash as the bond matures). The remaining banknotes can be redeemed for a share of the output produced by the maturing capital project. The old domestic agents must also pay a lump-sum tax.

As for the young in a given location, they accumulate cash equal to the sales of output to the old. After paying their taxes, the old collectively have cash balances equal to D. The young deposit this cash in their bank. The bank holds some cash back as reserves M and uses the rest to purchase newly-issued bonds B. The bank also uses some of its banknotes to purchase output P*k from the young workers, which the bank invests. At the end of this operation, the bank has assets M+B+P*k and a corresponding set of (demandable) liabilities. The broad money supply in this model is equal to M1 = M+B+P*k. The nominal GDP is given by NGDP = P*y + P*x*f(k).

Formally, I model the bank as a coalition of young agents. The coalition maximizes the expected utility of a representative member:  (1-s)*u(c1) + s*u(c2), where c1 is consumption in the domestic location and c2 is consumption in the foreign location. The maximization above is constrained by condition [4] which, expressed in real terms, can be stated as:

[5] y = m + b + k

where m = M/P and b = B/P (real money and bond holdings, respectively).

In addition, there is a budget constraint:

[6] (1-s)*c1 + s*c2 = x*f(k) + R*b + m - t 

where t = T/P (see condition [3]).

Finally, there is the "cash-in-advance" (CIA) constraint:

[7] s*c2 <= m

Note: the CIA constraint represents the "cash reserves" the bank has to set aside to meet expected redemptions. Because there is no aggregate risk here, the aggregate withdrawal amount is perfectly forecastable. This constraint may or may not bind. It will bind if the nominal interest rate is positive (i.e., R > 1). More generally, it will bind if the rate of return on bonds exceeds the rate of return on reserves. If the constraint is slack, I will say that the bank is holding "excess reserves." (with apologies to Nick Rowe).

Optimality Conditions

Because bonds and capital are risk-free and equally illiquid, they must earn the same real rate of return:

[8] R = xf'(k)

The bank constructs its asset portfolio to equate the return-adjusted marginal utility of consumption across locations:

[9] R*u'(c1) = u'(c2)

Invoking the government budget constraint [3], the bank's budget constraint [6], reduces to:

[8] (1-s)*c1 + s*c2 = x*f(k) + b + m 

In equilibrium,

[9] m = M/P and b = B/P

We also have the bank's budget constraint [4]:

[10] y = m + b + k

Because the  monetary authority is targeting a bond/money ratio z, we can use [2] to rewrite the bank's budget constraints [8] and [10] as:

[11]  (1-s)*c1 + s*c2 = x*f(k) + (1+z)*m 

[12] y = (1+z)*m + k

Finally, we have the CIA constraint [7]. There are now two cases to consider.

Case 1: CIA constraint binds (R > 1).

This case occurs for high values of x. That is, when the expected return to capital spending is high. In this case, the CIA constraint [7] binds, so that s*c2 = m or, using [12],

[13] m = (y - k)/(1+z)

Condition [11] then becomes (1-s)*c1 = xf(k) + z*m. Again, using [12], we can rewrite this as:

[14] (1-s)*c1 = x*f(k) + A(z)*(y - k)

where A(z) = z/(1+z) is an increasing function of z. Combining [8], [9], [13] and [14], we are left with an expression that determines the equilibrium level of capital spending as a function of parameters:

[15] x*f'(k)*u'( [x*f(k) + A(z)*(y-k)]/(1-s) ) = u'( (y-k)/(s*(1+z)) )

Now, consider a "loosening" of monetary policy (a decline in the bond/money ratio, z). The direct impact of this shock is to decrease c1 and increase c2. How must k move to rebalance condition [15]? The answer is that capital spending must increase. Note that since [8] holds, the effect of this "quantitative easing" program is to cause the nominal (and real) interest rate to decline (the marginal product of capital is decreasing in the size of the capital stock).

What is the effect of this QE program on the price-level? To answer this, refer to condition [4], but rewritten in the following way:

 [16] P = D/(y - k)

This is something I did not appreciate when I wrote my first post on this subject. That is, notice that the equilibrium price-level depends not on the quantity of base money, but rather, on the total stock of nominal government debt. In my original model (without capital spending), a shift in the composition of the D has no price-level effect (I erroneously reported that it did). In the current set up, a QE program (holding D fixed) has the effect of lowering the interest rate and expanding real capital spending. The real demand for government total government debt D/P must decline, which is to say, the price-level must rise.

[ Note: as a modeling choice, I decided to endogenize investment here. But one might alternatively have endogenized y (through a labor-leisure choice). One might also have modeled a non-trivial saving decision by assuming that the young derive utility from consumption when young and old. ]

Case 2: CIA constraint is slack (R = 1).

This case occurs when x is sufficiently small -- i.e., when the expected productivity of capital spending is diminished.  In this case, the equilibrium quantity of real money balances is indeterminate. All that is determined is the equilibrium quantity of real government debt d = m + b. Conditions [11] and [12] become:

[17]  (1-s)*c1 + s*c2 = x*f(k) + d 

[18] y = d + k

Condition [15] becomes:

[19] u'( [x*f(y - d) + d]/(1-s) ) = u'( d/s )

Actually, even more simply, from condition [8] we have xf'(k) = 1, which pins down k (note that k is independent of z). The real value of D is then given by d = y - k. [Added July 10, 2014]. 

Condition [19] determines the equilibrium real value of total government debt. The composition of this debt (z) is irrelevant -- this is a classic "liquidity trap" scenario where swaps of two assets that are perfect substitutes have no real or nominal effect. The equilibrium price-level in this case is determined by:

[20] P = D/d

A massive QE program in case (a decline in z, keeping D constant) simply induces banks to increase their demand for base money one-for-one with the increase in the supply of base money. (Nice Rowe would say that these are not "excess" reserves in the sense that they are the level of reserves desired by banks. He is correct in saying this.)

The question I originally asked was: do these excess reserves (as I have defined them) pose an inflationary threat when the economy returns to "normal?"

Inflationary Risk

Let us think of  "returning to normal" as an increase in x (a return of optimism) which induces the interest rate to R >1. In this case, we are back to case 1, but with a lower value for z. So yes, as illustrated in case 1, if z is to remain at this lower level, the price-level will be higher than it would otherwise be. This is the sense in which there is inflationary risk associated with "excess reserves" (in this model, at least).

Of course, in the model, there is a simple adjustment to monetary policy that would prevent the price-level from rising excessively. The Fed could just raise z (reverse the QE program).

In reality, reversing QE might not be enough. In the model above, I assumed that bonds were of very short duration. In reality, the average duration of the Fed's balance has been extended to about 10 years. What this means is that if interest rates spike up, the Fed is likely to suffer a capital loss on its portfolio. The implication is that it may not have enough assets to buy back all the reserves necessary to keep the price-level in check.

Alternatively, the Fed could increase the interest it pays on reserves. But in this case too, the question is how the interest charges are to be financed? If there is full support from the Treasury, then there is no problem. But if not, then the Fed will (effectively) have to print money (it would book a deferred asset) to finance interest on money. The effect of such a policy would be inflationary.

Finally, how is this related to bank-lending and private money creation? Well, in this model, where banks are assumed to intermediate all assets, broad money is given by M1 = D + P*k. We can eliminate P in this expression by using [16]:

[21] M1 = [ 1 + k/(y-k) ]*D

So when R > 1, reducing z has the effect of increasing capital spending and increasing M1. In the model, young agents want to "borrow" banknotes to finance additional investment spending. But it is not the increase in M1 that causes the price-level to rise. Instead, it is the reduction in the real demand for total government debt that causes the price-level to rise.

Likewise, in the case where R = 1 and then the economy returns to normal, the price-level pressure is coming from the portfolio substitution activity of economic agents: people want to dump their money and bonds in order to finance additional capital spending. The price-level rises as the demand for government securities falls. The fact that M1 is rising is incidental to this process.

Sunday, June 22, 2014

Excess reserves and inflation risk

Dave Wheelock, my colleague at the St. Louis Fed, points me to this nice article: Repeat After Me: Banks Cannot and Do Not "Lend Out" Reserves (by Paul Sheard). I have noticed a few papers lately making the same general point. I thought I'd throw my own two cents worth in.

To begin, you have probably seen (or heard about) this scary picture (thank you, "Helicopter" Ben):

That's a picture of the U.S. monetary base--the liabilities of the Federal Reserve Bank consisting of either currency or currency-on-demand (held by private, not government agencies). The monetary base can be divided into two broad categories: [1] currency in circulation (currency held by the non-bank private sector); and [2] reserves (bank sector vault cash and credits in reserve accounts held at the Fed).

In light of the "explosion" of Fed money since 2008, it may seem surprising that inflation has averaged considerably less than the Fed's official 2% target:

A common explanation for this is that most of the new money created by the Fed is being held by banks as reserves. Banks would rather earn 25 basis points (IOER) than lend out their excess reserves.

The following diagram depicts the liability side of the Fed's balance sheet:

We see that currency in circulation has increased, but at a modest and steady pace. Most of the increase in base money (remember, green part not included in money base) consists of reserves. The inflation fear expressed by some rests on the question of what is likely to happen once the economy returns to "normal." Sooner or later, things are going to turn around and banks will want to lend out their excess reserves to earn a higher rate of return. What is going to happen when this tidal wave of money begins to circulate?

According to Paul Sheard, this line of thinking is all wrong. That is, while monetary policy may ultimately result in higher inflation (or not), if it does, it won't be through the "banks lending out their excess reserves" channel, as many seem to suggest.

To understand his point, let's begin with how the Fed actually creates money. The Fed is a bank. And like all banks, it buys (or lends against) high-interest assets, which it finances by issuing low-interest liabilities (profits are returned to the Treasury). When the Fed buys a security on the open market, it credits the seller's bank account with newly-issued electronic digits (reserves). Banks then have the option of redeeming their reserves for currency, an option they may exercise depending on their customers' demand for currency.

Now, individuals regularly make deposits and withdrawals of cash into and out of their bank accounts. The net flow of withdrawals minus deposits determines by how currency in circulation grows over time. Banks do not lend out their cash. When a bank makes a loan, it issues a deposit liability that is redeemable for cash on demand. The demand deposit liabilities can be used as a payment instrument (they constitute money, and are counted as part of a broader measure of money supply, e.g., M1). The key observation here is that the way currency enters the economy is through the net withdrawal activity of bank customers--it has nothing to dow with banks lending out their reserves.

Alright, so why is understanding all this important? Well, for one thing, it is an accurate description of the way money and banking actually works (as opposed to the traditional "money multiplier" story that is commonly told in undergraduate textbooks). It is the right place to start when thinking of policy questions.

In terms of thinking about the inflation risk associated with the size of the Fed's balance sheet, it guides us away from examining how bank lending (the money multiplier) may react to various shocks. Banks can try to lend out their reserves all they want (create new loans). But if the public is satisfied with their currency holdings, any money injected into the system in this manner would have no effect on bank sector reserves. Since it is bank customers that determine how much cash is withdrawn from reserves, we should instead think about the type of shocks that may potentially alter this redemption decision.

To begin, we have to think about a world in which the asset side of the Fed's balance sheet matters. In many macroeconomic models, it is implicitly assumed that the Fed has full support of the Treasury (e.g., lump-sum taxes can be used to drain the economy of excess money), so that the Fed balance sheet does not matter. We want to do away with that assumption. In this case, the only "money draining" tools available to the Fed are asset sales. That is, think about the asset side of the Fed's balance as a giant vacuum cleaner. The amount of power this vacuum has is related to the market value of the Fed's asset portfolio. Any shock that would significantly reduce the market value of the Fed's asset portfolio would be like having your vacuum cleaner malfunction (just when you needed it the most).  

So, what type of shock can we think about here that might lend credence to the idea that excess reserves pose an inflation threat? I'm not really sure, but maybe the story goes something like this. Suppose that inflation expectations suddenly become "unanchored." (for whatever reason, people expect higher inflation). Through the Fisher equation, we might expect a large increase in nominal interest rates. The spike in interest rates would imply a capital loss for the Fed. By how much? Consider this formula (an approximation):

1 ppt increase in interest rate = (average duration)% decline in asset price. 

The average duration of the Fed's asset portfolio is roughly 10 years. So a five percentage point increase in interest rates would induce a 50% decline in the value of the Fed's assets (actually, somewhat less than this, but you get the point).

Now, higher inflation expectations on the part of the public may induce people to want to hold more currency (in nominal terms--the demand for real money balances may decline). This may be what could trigger a mass wave of redemptions. As people start withdrawing cash from their bank accounts, the banks start redeeming their reserves for cash to meet their customers' demands. The spike in interest rates unplugs the Fed's vacuum cleaner -- people know that the Fed does not have the tools to buy back all of its reserve liabilities. The wave of redemptions proceeds unchecked, with the flood of currency generating an inflation that becomes a self-fulfilling prophesy.

Well, that's just a story. I'm not sure if it hangs together logically (I've never seen it modeled formally, though perhaps it has been?) And even if it has a logical foundation, I'm not sure how persuasive it is. I am curious to know what other story one might tell. However the story unfolds, it cannot be one of bank lending out their reserves. 

Thursday, June 19, 2014

How far are we from trend?

I am always amazed at how well a log-linear trend line seems to fits real GDP (or per capita GDP) in the United States. Through a great depression, sandwiched by two world wars, secular changes in the relative importance of different sectors (agriculture, manufacturing, services), the baby boom, the increase in female labor force participation, etc. Through it all, the U.S. economy just seems to revert to the same log-linear trend. Maybe it was just a fluke. Whatever the case may be, that trend seems to have broken down since the great recession. We've all seen the diagram (the red line in the graph below -- thanks to my colleague Fernando Martin for the nice pictures).

The red line above plots the real GDP per capita (log scale) since 1955. The trend line is calculated over the sample period 1955-2007. The average growth rate is 2.2% per annum. You can see the big "output gap" emerging in 2008.

But given what we know about U.S. demographics--in particular the large rise, then fall in labor force participation, is the red line really the best way to look at things? A rough way to control for demographics is to consider the real GDP as a ratio of the labor force, instead of population. That is what the blue line does above. Once again, the trend line is computed for the same period 1955-2007. The average growth rate here is 1.5% per annum. What this tells us is that a lot of our measured growth over this period was due to nonstationary labor force behavior, and not just productivity. Oh, and the output gap near the end of the sample is considerably smaller. (It is too small to the extent that the recent decline in the labor force is attributable to "discouraged workers" who plan to return once conditions improve.)

Here is the same analysis for Canada:

The average growth rates are 1.7% (red) and 0.9% (blue), per annum. The blue line suggests that the Canadian economy is right on trend.
I think it's instructive to compare the U.S. to Canada. Consider, for example, the employment-to-population ratio for males aged 25-54:

There is a modest secular decline in the employment ratio in both countries.The Canadian employment ratio is currently not too far from its historical average, while the U.S. number still has some way to go. Of course, the great recession hit the U.S. much harder than Canada. Canada's great recession began in 1990 and it took about a decade for that economy to recover.

I began thinking about the similarity of the recent U.S. experience with Canada's earlier experience in this post: The Great Canadian Slump: Can it Happen in the U.S.? I followed up with a cross-country comparison of labor market behavior through the two episodes here: Employment Slumps in Canada and the U.S. Let me update the data there for males aged 25-54:

If the Canadian experience through the 1990s (red line) serves as a guide, then employment growth in the U.S. (blue line) will remain in recovery mode for another 4 or 5 years. While much of the gap has already been filled (it is not as dramatic as the first diagram suggests), there is still a considerable way to go when one looks at employment (instead of unemployment). So perhaps we are closer, but not as close to our goals as Jim Bullard suggests here: A Tame Taper.

Sunday, May 18, 2014

G and I in Europe and Japan

Izabella Kaminska reports here on a Credit Suisse comparison of Japan and the Euro area (h/t Scott Sumner). Here is an interesting diagram from that report:

According to Kaminska:
As the analysts note, a powerful fiscal stimulus in Japan helped to counter the demand shortfall. That caused personal consumption to continue to grow until 1997 and investment to rebound almost to its previous peak in just six years — something which isn’t slated for Europe any time soon.

Well, the increase in G counteracting an unexplained decline in I is one interpretation. This is the "deficient demand" interpretation that so many like to portray as obvious. But in fact, it's difficult to ascertain the direction of causality from just a picture.

The Japanese data above corresponds to what I posted some time ago here: What's Up with Japan? In response to that post, Mark Sadowski alerted me to the fact that the Japanese investment series plotted above includes both private and government spending. Here's what things look like when we decompose this aggregate (I discuss in more detail here: Another look at the Koizumi boom):

So it seems that there was a boom in private investment during the Koizumi years (something that Krugman gets wrong here, and something I'm not sure he's acknowledged). Moreover, this boom coincided with a slowing or outright contraction in government purchases. And in a liquidity trap era, I might add! What do our conventional "deficient demand" theories have to say about this? Maybe there is something more complicated than a simple IS-LM+liquidity trap story going on? I'm just asking. Humbly yours, DA.