## A Guest post by Ian Schindler (Schinzy)

This is an update to the post An Empirical Model For Oil Prices and Some Implications in which we discussed a model for oil prices as a function of 3 years of production, that is oil price in year t was estimated by production in year t, the discrete first derivative of production in year t, and the discrete second derivative in year t. We subsequently published a paper titled Oil Extraction, Economic Growth, and Oil Price Dynamics using the same model. This article contains most of our intuition on how peak oil will effect oil prices. We believe in fact that peak oil is about extraction prices rising faster than market prices and hence lower profitability for the oil industry.

Before going on, we note that all available data is very approximate. Jean Laherrère has exhaustively documented incoherence in extraction data from all standard sources [1]. We use a single price of oil provided by BP, but there is a large spectrum of prices for oil of different densities, chemistry, and provenance [2]. For this reason we do not search a perfect fit but rather try to understand the dynamics creating oil demand.

Inspired by work of Gail Tverberg and Rune Likvern on interest rates and oil prices, we added interest rates to the independent variables. Without interest rates, we had an adjusted R squared of .55.

We used extraction and price data from BP. The interest rate is the average yearly rate of the U.S. Federal Reserve. The justification for using this rate is that we believe that the U. S. dollar is the currency of oil markets and the U.S. Fed rate is the effective rate for the oil business.

The model is identical with the model discussed in *An Empirical Model For Oil Prices and Some Implications* with the exception that we have replaced the constant with the interest rate. Specifically our model is

**log(P(t)) = a* I(t) + b*Q(t) + c*DQ(t) + d*DDQ(t)**

or equivalently

**P(t) = exp( a* I(t) + b* Q(t) + c* DQ(t) + d* DDQ(t)),**

where P(t) is the price in year t, I(t) is the federal funds or interest rate in year t, Q(t) is the quantity extracted in year t, DQ(t) = Q(t)-Q(t-1), DDQ(t) = Q(t)-2Q(t-1) + Q(t-2) and the constants a, b, c, and d are estimated by linear regression.

The values of the regression coefficients are a = 1, b= .05, c=-.14, and d=.07. The largest coefficient is that of the interest rate, but of course interest rate numbers are small compared to production numbers. Thus once again, we find that the largest contribution comes from the first discrete derivative. R-squared adjusted is .9872, that is to say as high as can be expected with this quality data.

Below are charts of price versus the rate of extraction from 1965 to 2015, the federal funds rate versus the year, and the real and fitted price versus the year.

We have some ideas on what this model is saying, but we would rather say nothing for the time being and leave the interpretation for the comments section.

Bibliography

1

Laherrère J.

Fiabilité des données énergétiques.

Club de Nice treizième Forum annuel (2014).

2

Jean Laherrère.

Tentitives d’explication du prix du pÃ©trole et du gaz.

ASPO France, 2015. http://aspofrance.viabloga.com/files/JL_Nice2015long.pdf