Underestimating Exponential Growth

"The greatest shortcoming of the human race is our inability to understand the exponential function." 
-Albert A. Bartlett

Exponential growth is often widely underestimated. Here are a few issues where many people make mistakes because they don’t understand the simple math of exponential growth.

  1. Economic Growth: When there are trade offs between efficiency and equality, many people today think that the taxes, regulation and redistribution are worth a slightly lower growth rate.  However, when this trade off is applied over a long time period, the results can be staggering. If the choice was made in 1870 to have more equality at a cost of 1 percentage point of growth a year, America in 1990 would be no richer than Mexico.
  2. Entitlement Spending and National Debt: As I have pointed out previously, the United States is headed for very high debt levels if entitlement spending is not reformed.  One very simple way to fix this is to index entitlement benefits to inflation and not income. The growth of the economy would make it easy to pay for a safety net at today’s living standards. Unfortunately, this would only work for Social Security and not Medicare as the medical system is structured in a way that leads to health care inflation greater than that of the real economy.  Additionally, there is another problem when the net national debt reaches 100% of GDP. If the market perception of the debt turns negative and nominal interest rates remain higher than nominal GDP growth, then there is no way for the economy to grow itself out of debt.  This is the current situation with Greece, and Japan isn’t doing too much better.
  3. Personal Finance and Pension Plans: If a prudent investor can make 10% real returns in a year, then they can turn 50 thousand dollars into over 1.6 million dollars after 35 years. This simple math explains how many of the rich people today consist of those who have saved and invested prudently. On the other hand, a supposedly fully funded pension fund planning on a world of 8% real returns that finds itself in a world of 4% real returns will find itself underfunded by over 75% 35 years later (In this case, the people making pension return assumptions are underestimating how much they matter, they just know that their books look better if they assume a higher return). Robin Hanson has been proposing that people don't give to the future because they don't care about it, but it may also be that they do not fully understand the impact of exponential growth*.
  4. Overpopulation and increasing Resource Consumption: Overpopulation does not seem to be the exponential problem that we once thought it was. Once become rich enough, their population growth rate slows down. The UK’s Ministry of Defense 2008 Strategic Trends report expects the population to level out at around 9 billion people between 2050 and 2100 (page 25).  While overpopulation is itself not a problem, the exponential economic growth of these emerging economies are coincident with an exponential increase in demand for resources and these limited resources present constraints on growth.

Having established that exponential growth rates are important, here is a handy rule of thumb that will give an intuitive understanding of exponential growth. To calculate the doubling time of an exponentially growing series, take 70 (or 69.3 to be exact) and divide it by the growth rate. This means that a 10% growth rate leads to a doubling every 7 years, a 7% growth rate is a doubling every 10 years and a 3.5% growth rate is a doubling every 20 years.

*It is also possible that someone who both cares about the future and understands exponential growth might think that there were existential problems for the current society that are significant enough to reduce the probability of a far future donation from ever paying off.

The Republican Party's Demographic Future

Stereotypes are often statistically significant, and that is why the relative and absolute decline of the white population is going to hurt the Republican Party. After the last four years the talk of a permanent Republican majority seems especially ridiculous, but even when the Republicans were in charge their long term prospects have been tentative at best.

Source: US Census

Of course, politics is more complicated than just white people vote republican and other people vote for democrats. In order to narrow down the results further, I averaged the CNN exit polls from 2008 and 2004 (Counting the Nader voters as Democrats) to get the table below. 






















Using this table and the US Census data, I generated the following projection:


This projection is obviously a bit off, as Republicans were equal or ahead of democrats in 2000 and 2004.

There are a few factors that bias the analysis towards making democrats appear stronger than they are:

  1. Minority voters are younger and lean more democratic.  Young voters don’t show up in the same numbers as older voters, so an age weighted analysis would show Republicans as better off.
  2. There is some amount of over counting of Hispanic voters, as many of the Hispanic population are illegal aliens and unable to vote.
  3. There is a possibility of over counting of Hispanic voters voting democratic and under estimating the extent to which non-Hispanic white voter’s lean republican because all Hispanic people in the census were assumed to act as if they were Latino. It is very likely that a significant fraction of the Hispanic population told exit polls that they were white instead of Latino.
  4. The Electoral College based system gives Republicans a chance to retain control of the senate and white house via the smaller states with white majorities for far longer than the above chart would suggest.

Even given the above irregularities, it is obvious that demographic trends mean Republicans face an uphill battle. Democrats get the minority votes by supporting entitlement programs that disproportionately benefit minorities. Republicans then imitate the democrats in order to try and get votes, a strategy that is generally ineffective in terms of netting votes and has the effect of permanently expanding the entitlement infrastructure. Brown’s win in Massachusetts may have temporarily halted healthcare reform, but the demographic trend means that victory is only temporary.

The only way demographics are on republican’s side is that the consistent increase in age based entitlement spending from Medicare and Social Security means that a few years down the line the government will not be able to afford any additional entitlement spending without making everyone pay for it.


Introductory Post

The goal of this blog is to focus on long term problems while avoiding the pessimistic bias by recognizing the positive impact of human ingenuity compounding over long time periods

I’ve free ridden off of some of the very insightful analysis of the blogosphere for some time. This blog is my attempt to get some of my ideas out there and free ride off of the insightful commenters.

Below are a few of the themes that I think are important:

1. The time preference of the average person and average policy maker

There is a problem with the excessive focus on the short term. The existence of this focus is well documented in behavioral economic studies of hyperbolic discounting.  Policies that have tradeoffs with benefits in the short term vs. large expenses in the long term are often favored.  To take one example, the current state and local pension problems occurring all around the United States exist in part because the time preferences of politicians are far too short term.  Further more, demographic pressures mean that Keynes’s famous quote “The long run is a misleading guide to current affairs. In the long run we are all dead.” is changing to “In the medium run we are all dead” for more and more voters as the population of the developed world ages.

2. Globalization and its impact on the middle class of the developed world

Globalization is unequivocally increasing the wealth of this world. Basic comparative advantage proves that when trade is opened up, the pie grows. However, the inefficient producers of goods produced by new trading partners do often lose out. In this day and age, those inefficient producers tend to consist largely of the middle class of the developed world. The upper class has capital that is benefiting from globalization while the lower class has service jobs with manual labor that can’t be replicated by someone working for much cheaper when they are halfway across the globe.  The interesting question is whether the benefits of cheaper goods outweigh the costs of slightly worse jobs for the middle class.  Even with globalization, total compensation has been trending upwards for labor, people just don’t notice it because a lot of compensation goes towards labor costs and many simplistic commentators like showing the inflation adjusted household median income chart that leaves out noncash forms of compensation.  

Source: US Census and BLS

The other question is whether there is any policy that could have prevented these harms to the middle class short of attempts to keep the developing world undeveloped.  Even if the answer to that is no, this does not mean that there will not be a counter productive political attempts to reverse recent trends.

3. Resource constraints

Peak oil is the main resource constraint that comes to mind, but there are many long term issues with resources that are not being adequately addressed. Peak oil generally raises the cost of substitutable goods, making other forms of energy more expensive. This bleeds into other assets such as raising the cost aluminum, which is produced in an energy intensive fashion.  Water constraints are another important resource limitation on growth.  Other resources like rare earth elements or industrial metals may be more expensive due to short term supply and demand imbalances driven in part by the developing world. What makes peak oil more interesting than other basic resource problems is that the daily oil supply is running up against geologic constraints while other resource shortages generally last only as long as it takes for new mines to be built and brought online.

4. The entitlement mindset

A lot of people feel like they are owed a lot of things by society. They also believe that the average person shouldn’t be paying for these things. This is a trend that cannot continue.  Also relevant to this theme is the long term performance of countries with lots of foreign aid compared to countries that are less dependent on foreign aid.

5. Status driven trends

As the developed world gets richer, more and more money is spent on status and signaling related behavior. This has many unfortunate side effects.

6. Demographic issues

Source: UN Medium Variant Projections: The 2008 Revision

Charts like the one above are very common when discussing upcoming demographic problems.  The developed world is aging, and long term demographic trends are important beyond the basic “How are we going to pay for all of these old people?” questions.