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

Code platform update

It’s a week away from 2015, and I have transitioned completely away from Matlab. Julia is winning the platform attention battle. It is very easy to code in and it is very fast. I just haven’t gotten around to learning python much less pyDSTool (sorry Rob). I kind of find the syntax of Python (with all the periods between words) annoying. Wally Xie and I have also been trying to implement some of our MCMC runs in Stan but we have had trouble making it work.  Our model requires integrating ODEs and the ODE solutions from Stan (using our own solver) do not match our Julia code or the gold standard XPP. Maybe we are missing something obvious in the Stan syntax but our code is really very simple. Thus, we are going back to doing our Bayesian posterior estimates in Julia. However, I do plan to revisit Stan if they (or we) can write a debugger for it.

New paper in eLife

Kinetic competition during the transcription cycle results in stochastic RNA processing

Matthew L FergusonValeria de TurrisMurali PalangatCarson C ChowDaniel R Larson


Synthesis of mRNA in eukaryotes involves the coordinated action of many enzymatic processes, including initiation, elongation, splicing, and cleavage. Kinetic competition between these processes has been proposed to determine RNA fate, yet such coupling has never been observed in vivo on single transcripts. In this study, we use dual-color single-molecule RNA imaging in living human cells to construct a complete kinetic profile of transcription and splicing of the β-globin gene. We find that kinetic competition results in multiple competing pathways for pre-mRNA splicing. Splicing of the terminal intron occurs stochastically both before and after transcript release, indicating there is not a strict quality control checkpoint. The majority of pre-mRNAs are spliced after release, while diffusing away from the site of transcription. A single missense point mutation (S34F) in the essential splicing factor U2AF1 which occurs in human cancers perturbs this kinetic balance and defers splicing to occur entirely post-release.