# The liquidity trap

The monetary base (i.e. amount of cash and demand deposits) has risen dramatically since the financial crisis and ensuing recession.

Immediately following the plunge in the economy in 2008, credit markets seized and no one could secure loans. The immediate response of the US Federal Reserve was to lower the interest rate it gives to large banks. Between January and December of 2008, the Fed discount rate dropped from around 4% to zero but the economy kept on tanking. The next move was to use unconventional monetary policy. The Fed implemented several programs of quantitative easing where they bought bonds of all sorts. When they do so, they create money out of thin air and trade it for bonds. This increases the money supply and is how the Fed “prints money.”

In the quantity theory of money, increasing the money supply should do nothing more than increase prices and people have been screaming about looming inflation for the past five years. However, inflation has remained remarkably low. The famous bond trader Bill Gross of Pimco essentially lost his job by betting on inflation and losing a lot of money. Keynesian theory predicts that increasing the money supply can cause a short-term surge in production because it takes time for prices to adjust (sticky prices) but not when interest rates are zero (at the zero lower bound). This is called a liquidity trap and there will be neither economic stimulus nor inflation. The reason is spelled out in the IS-LM model, invented by John Hicks to quantify Keynes’s theory. The Kahn Academy actually has a nice set of tutorials too. The idea is quite simple once you penetrate the economics jargon.

The IS-LM model looks at the relationship between interest rate r and the general price level/economic productivity (Y). It’s a very high level macroeconomic model of the entire economy. Even Hicks himself considered it to be just a toy model but it can give some very useful insights. Much of the second half of the twentieth century has been devoted to providing a microeconomic basis of macroeconomics in terms of interacting agents (microfoundations) to either support Keynesian models like IS-LM (New Keynesian models) or refute it (Real Business Cycle models). In may ways this tension between effective high level models and more detailed microscopic models mirrors that in biology (although it is much less contentious in biology). My take is that what model is useful depends on what question you are asking. When it comes to macroeconomics, simple effective models make sense to me.

The IS-LM model is analogous to the supply-demand model of microeconomics where the price and supply level of a product is set by the competing interests of consumers and producers. Supply increases with increasing price while demand decreases and the equilibrium is given by the intersection of these two curves. Instead of supply and demand curves, in the IS-LM model we have an Investment-Savings curve and a Liquidity-Preference-Money-supply curve. The IS curve specifies Y as an increasing function of interest rate. The rationale  that when interest rates are low, there will be more borrowing, spending, and investment and hence more goods and services will be made and sold, which increases Y.  In the LM curve, the interest rate is an increasing function of Y because as economic activity increases there will be a greater demand for money and this will allow banks to charge more for money (i.e. raise interest rates). The model shows how government or central bank intervention can increase Y. Increased government spending will shift the IS curve to the right and thus increase Y and the interest rate. It is also argued that as Y increases, employment will also increase. Here is the figure from Wikipedia:

Likewise, increasing the money supply amounts to shifting the LM curve to the right and this also increases Y and lowers interest rates. Increasing the money supply thus increases price levels as expected.

A liquidity trap occurs if instead of the above picture, the GDP is so low that we have a situation that looks like this (from Wikipedia):

Interest rates cannot go lower than zero because otherwise people will simply just hold money instead of putting it in banks. In this case, government spending can increase GDP but increasing the money supply will do nothing. The LM curve is horizontal at the intersection with the IS curve, so sliding it rightward will do nothing to Y. This explains why the monetary base can increase fivefold and not lead to inflation or economic improvement. However, there is a way to achieve negative interest rates and that is to spur inflation. Thus, in the Keynesian framework, the only way to get out of a liquidity trap is to increase government spending or induce inflation.

The IS-LM model is criticized for many things, one being that it doesn’t take into account of dynamics. In economics, dynamics are termed inter-temporal effects, which is what New Keynesian models incorporate (e.g. this paper by Paul Krugman on the liquidity trap). I think that economics would be much easier to understand if it were framed in terms of ODEs and dynamical systems language. The IS-LM model could then be written as

$\frac{dr}{dt} = [Y - F]_+ - r$

$\frac{dY}{dt} = c - r - d Y$

From here, we see that the IS-LM curves are just nullclines and obviously monetary expansion will do nothing when $Y-F <0$, which is the condition for the liquidity trap. The course of economics may have been very different if only Poincaré had dabble in it a century ago.

2104-12-29: Fixed some typos

## 4 thoughts on “The liquidity trap”

1. comments—-i glance at alot of economics blogs and other things. this is partly because i was interested in applications of stat mech to biology and came across ‘gibbs ensemble, biological ensemble’ by E Kerner (who also had a kind of VSL theory in the 60’s) in old Bull Ma Bio journals (from the early 60’s; for a brief period the editor of that journal had the office next to the computer lab i was working in). I found papers by Paul Samuelson (economics) in PNAS around 1973 combining Kerner’s model with one by Richard Goodwin (economics) on marxism, called the ‘class struggle model’ based on Lotka-Volterra equations. Thats my style of econ (and it crops up here and there—s keen, and someone at U Md has variants which made a splash for awhile last year in the press). You get all or most of Marxism in 2 equations—you don’t need to read Das Kapital etc. .

(Kerner’s model was discussed by Robert May also, and especially its limitations—-though there were papers up to the 90’s etc on whether one could find ‘hamiltonians’ and conservation laws for lotka-volterra type systems of equations—there’s a ton of these papers, alot out of russia. D Ludwig also had stuff on ‘stochastic lagrangians’ etc. in biology in the 70’s..) . (I found these old papers since when i go to a library i pick up old issues of journals just randomly on top of what i’m supposedly looking for—its amazing what you find (especially old Rev Mod. Phys from the 40’s and 50’s).

A favorite econ paper i have is from 1938 by H T Davis in Am Math Monthly; goes through standard utility calculus, and also analogies between mechanics and economics (a matter of contention—see Mirowski, or J B Rosser). One of the first was by Fischer who was a student of Gibbs. (Another good one is by eugene slutsky also from the 30’s on spurious correlations and cycles—it can be interpreted as saying that the ‘great depression was, like chaos, just due to computer roundoff error or the way you chose your ‘moving averages’ for time series (which is actually the Lucas RBC critique—there’s no involuntary unemployment). Sure, you can say there was a great depression or anything else just as you may be able to say 1+2+3+4+…= – 1/12 or whatever you want it to be. I had an old book by Max Born on relativity; he was discussing the speed of light and said (i think in agreement with Poincare) ‘the speed of light can have any value you want it to have’ but pointed out the convention (due to an Occam’s razor argument) is its a fixed universal constant. (eg h=c=i=G=beta=it=…1.)

I cant even remember what all the P, Y, r, C, F etc. terms mean in economics—i have to look them up each time.Maybe its easier in Python or Farsi dialects. Math econ seems to have a very clumsy formalism. (If it was developed scientifically, perhaps it would have a very clear and unambiguous formalism and applicability like the US Consititution which was developed around 1780 in the Bourbaki tradition of axiomatic logic (though it uses ‘Paraconsistant logic’, so things like abortion, gay marriage, smoking cannabis, interracial marriage, slavery, etc’ are both legal and illegal. (see also L Kuaffman on laws of form). One good thing about clumsy formalism is it may be a simply algorithm—you can just muddy the waters on the floor of congress, on CSPAN, or in a journal and get paid for doing something.

Yakovenko (U Md) ‘s papers on stat mech of money’ made a splash and are suggestive of something, though its unclear what. (Alot of income follows a boltzmann distribution and arrives through essentially random transfers. Unfortunately, this means you get a Gini of .5 always, but on the other hand because of ergodicity everyone will get their ’15 minutes of welath and fame ‘ (warhol) once in a while before sinking back into the more probable configurations of phase space of poverty. Slowly people are trying to combine the stat mech random/entropy models in econ with the traditional ‘mechanical’ ones based on utility maximization, optimal allocation of resources, etc. though the twain may never meet. Also its possible that you will end up with two different kinds of mechanisms (one deterministic, one statistical) which lead to identical results (eg Ornstein and Weiss BAMS ’91—i have seen 2 economics papers that cite that result). (Entropic gravity seems to unify the 2 mechanisms, but who knows what that means).

It is sad that the liquidity trap (which I gather QE was supposed to cure) is leading to a loss of productive resources—think of how many trucks could be using the Tar Sands of Canada to deliver bottled water and coca cola so the social welfare function could reach its maximum value. Instead we’re stuck in a ‘poverty trap’ (eg S Durlauf—who also had a paper on stat mech applied to econ in an old SFI volume).

Like

2. Rick G says:

In the liquidity trap scenario (locally flat LM curve), the Fed can print money and buy resources, including the rest of the world’s resources if needed at absolutely no cost (i.e. no inflation). At some point the Fed either gets the target amount of inflation (which was the goal) and then stops, or they don’t ever get that level of inflation but own the entire world. These are the only two scenarios compatible with this model (with other possibilities as you add dynamics).

So at least in this model, the liquidity trap isn’t an actual economic problem, it’s a political problem. The amount of QE required to actually generate inflation might be so large that Congress would object and try to get a law passed to change the Fed’s mandate, or otherwise throw up attempted political roadblocks. But those same obstacles are there with fiscal stimulus as well. The difference is that fiscal stimulus increases debt and monetary stimulus (at the zero bound) doesn’t.

So I interpret Krugman’s advocacy of fiscal stimulus in a liquidity trap as his naked political preference for more government spending, and his opponent’s preference for monetary stimulus as at least partly couched in the opposite preference. Celebrity economists (even Nobel laureates) entire public careers and reputations depend upon their engineering justifications for what one political party or another is going to do anyway, so this shouldn’t be a huge shock.

Like

3. Rick G says:

Then there’s the fact that Japan did successfully inflate after 20 years of being in a supposed liquidity trap, Switzerland did successfully devalue their currency against the Euro, the US economy did grow robustly in the face of the sequester and relative austerity, etc., all events that Krugman predicted to be impossible because of so-called liquidity traps in those countries. In all cases, all that seemed to matter was what long run price level trajectory the public (i.e. investors) believed the associated central banks were committed to.

For example, if you really believed those central banks would do whatever it took to engineer, say, 2% inflation, then it would be foolish to bet against them because you would just lose all your money. They can print as little or as much money as needed to reach that goal. What is a liquidity trap in the face of that kind of power?

Anyway, Krugman certainly won the argument against more-or-less all of the right-wing inflation hawks, but he still looks pretty foolish against, say, Scott Sumner or any of the so-called market monetarists (not the old monetarists).

Like

4. @Rick Krugman advocated either fiscal policy or for the central bank to act “irresponsibly” so I don’t think he differs that much from Sumner and other market monetarists who advocated nominal GDP targeting. I do agree that it is as much a political problem as an economic one. Obviously, the model is incomplete if the government starts to buy an appreciable amount of the world.

Like