Friday, December 30, 2016

The Ghost of GDP Past

I can't look at a GDP decomposition without thinking of the old "What's Mozart doing? He's decomposing" joke.
I am so sorry.
From Newfound Research, Dec. 12. 2016:

This blog post is available as a PDF here
  • Economic growth is a key driver of long-term stock and bond returns.
  • Economic growth comes from two main sources: demographic changes (i.e. increases in the number of workers) and productivity growth (i.e. each worker producing more output). Historically, approximately 55% of growth has come from productivity growth and 45% has come from demographic changes.
  • Slowing population growth and an aging population make it unlikely that demographics will continue to be a strong tailwind to economic growth over the next 50 years.
  • Barring a productivity miracle, future economic growth is likely to disappoint those who anchor expectations to the past. Investors must adjust their expectations and strategies to fit this new reality.
Trend GDP growth is a critical determinant of traditional asset class returns.  For equities, GDP growth has historically served as an upper bound to earnings growth.  For bonds, short-term interest rates can be modeled as the sum of GDP growth, time preferences (i.e. the relative preference between saving and investment), and monetary policy effects.

When thinking about GDP growth, we prefer to follow an unbundle/re-build framework.  With this approach, we unbundle the sources of GDP growth, analyzing each both individually and in concert with the other sources of growth, and only then re-aggregate the components to top level GDP growth.

There are a number of valid methodologies for decomposing GDP growth.  In this piece, we will use a supply-side approach.  The basics are as follows.

In the equation below, let Y denote real GDP and N denote total population.  We can decompose real GDP per capita (Y / N, the amount of output/income produced on average by each member of the population) as follows:
where E is total employment and L is the working age population.

The first term on the right-hand side of the equation (Y/E) reflects the amount of output generated per worker.  This is a measure of productivity.  (Note: Productivity is typically measured as output per hour worked since output per worker can change simply due to fluctuations in hours worked.  For example, increases in part-time jobs as a proportion of total jobs would reduce hours worked and output per worker even though productivity was unchanged.  That being said, long-term output per worker trends have been driven almost entirely by changes in productivity.  As a result, we are comfortable using output per worker as a proxy for productivity.)

The second term (E/L) is the proportion of the working age population that is employed.  This will be a function of the labor force participation rate (the proportion of the population that wants to work) and the employment rate (the proportion of the labor force with a job, which equals one minus the unemployment rate).

The third term (L/N) is the percentage of the population that is of working age (16 years and older).
Using a mathematical tool called the Shapley decomposition, we can represent changes in real GDP per capita as a weighted average of changes in each of these three quantities.

Once we understand the sources of per capita GDP (Y / N) growth, we can easily pivot to total GDP (Y) growth since the growth rate in per capita GDP will be approximately equal to the difference between total GDP growth and population (N) growth.  Equivalently, total GDP growth will be approximately equal to the sum of per capita GDP growth and population growth.

A Case Study: Understanding Long-Term GDP Growth in the United States (1948 to 2015)
As a case study, let’s unbundle the sources of U.S. GDP growth from 1948 to 2015.  In 1948, real GDP was $2.0 trillion in 2009 dollars.  By 2015, real GDP had growth to $16.4 trillion, an annualized growth rate of 3.2%.
Summarizing U.S. Economic Growth (1948 to 2015)
Of this 3.2% growth, a little less than two-thirds (2.0%) resulted from more output per person (i.e. growth in real per capita GDP).  The remaining growth (1.2%) came simply from an increase in population.
We can go a step further by using the aforementioned Shapley decomposition to attribute the per capita GDP growth to changes in productivity (output per worker), changes in the employment rate (the percentage of the working age population that is employed), and changes in population composition (the percentage of the population that is of working age).
The vast majority (~89%) of per capita GDP growth can be attributed to increases in productivity.  In 1948, the average worker produced $34,613 worth of output.  This figure grew to $110,167 by 2015.  Changes in the employment rate and population composition combined to contribute just 0.23% to real per capita GDP growth.

To gain more intuition around the drivers of productivity growth, we can break it into two components:...MORE