Weather prediction

I think it was pretty impressive how accurate the predictions for Superstorm Sandy were up to a week ahead.  The hurricane made the left hand turn from the Atlantic into New Jersey just as predicted.  I don’t think the storm could have been hyped any more than it was.  The east coast was completely devastated but at least we did have time to prepare.  The weather models  have gotten much better from even ten years ago. The storm also shows just how vulnerable the east coast is to a 14 foot storm surge.  I can’t imagine what a 20 foot surge would do to New York.

Time constants in the economy

I was struck recently by a figure that economist Paul Krugman posted on his blog of the recovery time from recessions.

The interesting point to me was that there seems to be some consistency in the rate of recovery from different types of recessions. In other words, there are fixed time constants in the economy. A recession is defined as a period with negative GDP growth rate, i.e. it is a time when the economy shrinks.  Generally, the US has been growing a few percentage points a year in real terms for the past several decades. This is interrupted by occasional recessions such as a severe one in 1980-81 and the most recent Great Recession of 2008-2009.

However, not all recessions are created equal and economists have made a distinction between those caused by disinflation and financial crises.  An example scenario for a disflationary recession is that the economy is initially overheated so while there may be lots of growth there is also lots of inflation. The causes of inflation are complicated but they are sometimes linked to the interest rate. When rates are low, it is cheap to borrow, so people can acquire more money to spend and too much money chasing too few goods leads to inflation. A recession can then be induced by interest rates increasing, either through direct action by the Federal Reserve Bank or some exogenous factor, which makes it more expensive to borrow money and also incentivizes saving. This reduces the money supply.  This is what happened in the 1980-81 recession.  Inflation was extremely high in the 1970’s so Fed chairman Paul Volker dramatically increased interest rates. This induced a recession and also curbed inflation.  How the Fed controls interest rates is extremely interesting and something I may post about in the future. A recession can also be caused by no apparent external event if people simply decide to decrease spending all at once. A beautiful example is given by the famous story of a babysitting coop (see here). In a disinflationary recession, the economy can start growing if you can get people to start spending again. This can be done by lowering the interest rate or through a fiscal stimulus plan where the government starts to spend more. The time constant for recovery will be about the time it takes for people who lost jobs to find new ones and this is usually less than two years.

Recessions due to financial crises are generally preceded by a financial bubble where some asset, such as real estate, increases dramatically in price and then people, companies and banks take on more and more debt to try to make money by speculating on this asset. This is what happened in the run up to the Great Recession and the Japanese financial crisis in the 1990’s. When the bubble finally bursts, people are left with lots of debt and little money  to spend, thereby inducing a recession. In the case of real estate, the debt is in the form of mortgages, which are usually long term. The time constant will be the average duration of the mortgage or the time it takes to refinance. In both cases, this will take longer than two years. Thus, the recession will persist until people can pay off or unload their debts and both are difficult when the economy is depressed. It also shows why monetary policy may have little effect. Lowering interest rates can’t directly help the people trapped in long-term mortgages. However, if the interest rates can be kept low enough and long enough to induce some inflation then house prices increase while effective debt decreases so people can sell their homes or refinance and get more money to spend. This is basically what current Fed chairman Ben Bernanke is trying to do.  Another option would be for the federal government to take advantage of low interest rates and start buying property. They could have started a buy-and-lease program where underwater homeowners could sell their homes to the government and then rent it back from them. This would keep people in their homes, bolster the economy and also ensure that people who made bad decisions during the bubble do not profit from their mistakes. When house prices rise again, the government would pocket the profits.

Using formal logic in biology

The 2012 Nobel Prize in physiology or medicine went to John Gurdon and Shinya Yamanaka for turning mature cells into stem cells. Yamanaka shook the world just six years ago in a Cell paper (it can be obtained here) that showed how to reprogram adult fibroblast cells into pluripotent stem cells (iPS cells) by simply inducing four genes – Oct3/4, Sox2, c-Myc, and Klf4.  Although he may not frame it this way, Yamanaka arrived at these four genes by applying a simple theorem of formal logic, which is that a set of AND conditions is equivalent to negations of OR conditions.  For example, the statement A AND B  is True is the same as Not A OR Not B is False.  In formal logic notation you would write .  The problem then is given that we have about 20,000 genes, what subset of them will turn an adult cell into an embryonic-like stem cell. Yamanaka first chose 24 genes that are known to be expressed in stem cells and inserted them into an adult cell. He found that this made the cell pluripotent. He then wanted to find a smaller subset that would do the same. This is where knowing a little formal logic goes a long way. There are possible subsets that can be made out of 24 genes so trying all combinations is impossible. What he did instead was to run 24 experiments where each gene is removed in turn and then checked to see which cells were not viable. These would be the necessary genes for pluripotency.  He found that  pluripotent stem cells never arose when either Oct3/4, Sox2, c-Myc or Klf4 were missing. Hence, a pluripotent cell needed all four genes and when he induced them, it worked. It was a positively brilliant idea and although I have spoken out against the Nobel Prize (see here), this one is surely deserved.

2016-1-20:  typo corrected.

Revised SDE and path integral paper

At the MBI last week, I gave a tutorial on using path integrals to compute moments of stochastic differential equations perturbatively.  The slides are the same as the tutorial I gave a few years ago (see here).  I slightly modified the review paper that goes with the talk. I added the explicit computation for the generating functional of the complex Gaussian PDF. The new version can be found here.

Talk at MBI

I’m currently at the Mathematical Biosciences Institute at The Ohio State University at a workshop on Mathematical Challenges in Neural Network Dynamics.  My slides are here.

More on health care costs

I posted previously that the rising cost of health care may not be a bad thing if it ends up providing jobs for the bulk of the population.  The Economist magazine blog Free Exchange had an interesting piece on how health care can become both more expensive and more affordable simultaneously. The argument comes from William Baumol of Baumol’s cost disease, (of which I posted on previously here). In simple terms, Baumol’s argument is that as society gets more productive and richer the salaries of everyone goes up including those in professions, like art and health care, where productivity does not increase. Now, given that the bulk of costs of most sectors are salaries, productivity increases generally imply decreases in the number of people in that economic sector. At current rates of growth, health care expenditures will be 60% of US GDP by 2105. However, as long as the economy as a whole grows faster than the rate of increase in health care costs then we will still have plenty leftover to buy more of everything else. If we make the simple assumption that contribution to GDP is proportional to population then an increase in health care’s share of GDP simply means that the share of the population working in health care is also increasing. Basically, at current rates of growth, we will all become health care workers. I don’t think there is anything intrinsically wrong with this.  How a nation’s wealth is distributed among its population is more important than how it is distributed among sectors.