## Saturday, March 04, 2006

### How Probable is a US Recession if the Oil Supply is Shrinking?

This post is a little addition to the previous post "US Addiction to Oil". We looked at the annual variations of US oil consumption per capita and observed a significant correlation with the annual GDP per capita variations (see Figure 1 below). I propose to investigate a little bit more into that relationship. We note BCYV the number of Barrels per Capita per Year Variation and GCYV the GDP per Capita per Year Variation. Valleys on the GCYV curve are economic slowdown and recessions that have occured many times in the past when GCYV becomes negative. I surimposed on the graph the different major recession occurences that have affected the US economy. There was only two major oil supply contractions in the past: the 1973 oil embargo and the 1979-1980 Iranian crisis. They correspond to the two big drops below -4% on the BCYV curve.

Fig 1. Year-on-year variations of the GDP per capita (in blue) and the consumed oil barrels per capita (in red). The light dotted gray lines indicate recessions.

We use a bi-dimensional gaussian function to describe the joint probability distribution of GCVY and BCYV as shown on Figure 2.

Fig 2. Scatter plot of GCYV vs BCYV and the multivariate gaussian probability function. The blue dotted line indicate the principal direction of variation (first eigenvector).

The parameters (covariance matrix and mean vector) for the bi-dimensional gaussian estimated from the data are the following:

The blue line on Figure 2 is the principal component of the covariance matrix and corresponds to the following equation:

So, in average the US have enjoyed a nice 2.15% GDP growth since 1965. Now, let's compute some probability values from that model such as the probability of a recession (we note B=BCYV and G=GCYV):

We repeat this calculation for the case where BCYV > 0, the different values are shown on Figure 3. If the oil consumption per capita is shrinking we have a 30% chance of having a recession whereas the probability is only 2% if the oil consumption per capita is growing.

Fig 3. Probability values of a recession or a GDP growth having different oil consumption variations.

Of course, this a simplistic analysis and there are many other factors that can influence the GDP growth. Also, we didn't take into account the impact of energy conservation, efficiency and energy alternatives.

References: