Crude oil (NYSEARCA:USO)(NYSEARCA:OIL) is generally priced off traditional supply and demand analysis, as it is consumable, can be depleted, and does not act as an alternative currency or wealth preservation tool like gold (NYSEARCA:GLD) or silver (NYSEARCA:SLV).

Therefore, items like consumption and production should come in as statistically significant in any regression analysis being the fundamental elements of supply and demand. A ratio between consumption and production should be used in any model as well given that the magnitudes of each variable have grown in proportion to world population growth and economic/industrial development.

But what about other macroeconomic influences, such an interest rates and metrics representing components of overall government financial health? Real GDP for historically net-importing countries should normally enter into oil price regressions in a statistically significant manner and probably have a negative sign. As an input into economies, cheaper prices allow for higher margins and higher consequent growth and households will become slightly wealthier. For net-exporting countries it should be the opposite, given the fraction of corporate and/or government revenue that is contingent on crude prices.

I've found in the past that inflation rates (or expected inflation rates) in the largest, developed countries tends to have little influence on oil, given that the effect can work both ways. If the price of an input (such as oil) is higher, then producers will normally try to pass off as much of this cost as they can to consumers in the pricing of the output.

So for this exercise we can boil it down to consumption, production, a ratio between consumption and production, oil reserves, US real GDP, US inflation, and the federal funds rate (as a proxy for interest rates). I previously performed this exercise without considering influence of the federal funds rate, and when playing around with the data recently, found that interest rates have seemed to become more influential relationship with respect to crude prices over time.

Perhaps part of the effect may be attributed to the increased financialization of commodity markets over time. Commodity financialization refers to the inflow of capital into commodity futures markets largely due to a lack of attraction in other asset classes, pushing prices out of sync relative to what may be dictated by traditional supply and demand fundamentals. The sign of this variable could really go either way. It would not be a matter of investors pushing money into commodities because borrowing costs are cheap under the traditional interpretation of financialization. It could be that as interest rates risk and decrease the appeal of riskier assets (stocks, real estate) or other asset classes that appreciate as rates fall (fixed income), this incentivizes investors to find a different avenue to place their capital.

The elements of US current account and US fiscal surplus/deficit are also available in the dataset but aren't expected to come back as statistically significant.

**Data**

Data were gathered from the St. Louis Federal Reserve's economic database and the EIA. The data is aggregated at a quarterly level and runs from Q1 1986 to Q3 2016. For categories in which only annual data was available, such figures were entered in for all four quarters.

**Results**

My preliminary regression (standard ordinary least squares approach) yielded that US real GDP, the federal funds rates, and all the standard supply and demand variables came in as statistically significant. The elements of US inflation (as measured through a personal consumption expenditures price index (PCEPI)), current account and federal deficit/surplus were expectedly not significant.

(*Source: author*)

When throwing out all the non-significant variables we get the following:

(*Source: author*)

Everything is statistically significant at at least the 1% level, meaning that we can generally have 99% confidence that the influence of the predictor variables on the dependent (oil prices) is genuine.

If we take the natural logarithm of the price of oil, we obtain similar results.

(*Source: author*)

Using a natural log on the dependent variable has the benefit of reducing the influence of outliers in a positively skewed dataset and better normalizing the data in many cases. It also carries the benefit of being able to more easily interpret results, as the coefficients demonstrate the percentage change in the price of oil based on a one-unit change in a predictor variable. For example, the results above suggest that a one percentage-point increase in the federal funds rate would increase the price of oil by 3.3%.

In a log-normal model, which fits the natural logarithm of the dependent variable to a normal distribution rather than its actual numerical value to better handle outliers in the data, we see different results. This time, interest rates fail to meet any of the traditional levels of statistical significance with a p-value of just 0.15. Normally economists will dismiss the influence of such a variable if the p-value is above 0.05.

(*Source: author*)

Throwing out the federal funds rate produces the following:

(*Source: author*)

However, I am generally reluctant to form prediction models based on log-normal regressions, even if the supplementary statistics check out (e.g., high R squared, low AIC), given how sensitive the outputs tend be to the inputs.

If we parametrize the data based on a t-distribution, we might actually get a model that better resembles the actual distribution of the data. A common criticism of OLS's application to many forms of financial data lies in the fact that the normal distribution assumption that forms the basis of that regression type results in a flawed parameterization. Outliers tend to be more common in financial data than what might be predicted by a normal distribution, which makes a heavier-tailed distribution perhaps the better approach.

(*Source: author*)

Real GDP fails to meet the 5% significance level, but some researchers are willing to accept results significant at the 10% level. It's really a judgment call and depends on how much certainty one would like. I personally feel comfortable keeping it in, as it was significant in all other approaches tried up until this point.

Quantile regression, which estimates conditional median and other quantiles rather than the mean alone, was used for the fourth and final model type. The same set of variables were used:

(*Source: author*)

**Interpretation**

Clearly the supply and demand elements of the oil market dominate the regression results, as expected. Those who follow the oil market are fully cognizant of how price reacts to consumption, production, and reserves data. Increased consumption (demand) increases prices while increased production and reserves (supply) decrease prices. GDP and interest rate data out of the largest developed countries can be more difficult to ascertain the influence.

For some economies, such as those of some Mideastern countries, Russia, Libya, Algeria, Nigeria, and Venezuela, oil is a huge influence on GDP itself (i.e., oil being a predictor/"right-hand side" variable in itself).

For net importing countries, the relationship becomes a bit fuzzier. Does the price of oil increase, on net, when importing countries are undergoing growth surges, resulting in higher demand? Or do declining oil prices help increase economic growth because cheaper inputs help enhance consumer savings, expand corporate margins, and the financial health of businesses overall? There is probably some merit to both arguments. For whatever it's worth, real GDP had a positive coefficient in each of these models considering data at the quarterly level over the past thirty years.

Interest rates, using the effective federal funds rate, saw statistical significance in three of the four model types considered (all aside from the log-normal). High interest rates were observed to have a statistically significant impact on increasing the price of oil in the OLS, t-distribution, and quantile regression models.

Most of the effect is likely derived from the data stemming from this century. From 1986 to 2000, oil consistently traded at around $20 per barrel, outside of a brief doubling during the 1990-91 recession and an uptick in 1999. Oil consistently climbed as the Fed raised rates from 2004-06 before trending lower after interest rates were dropped to zero following the financial crisis. Oil traded above $100 per barrel in June 2014 before falling all the way to $26 per barrel just eighteen months later.

(*Source: US. Energy Information Administration; modeled by fred.stlouisfed.org*)

(*Source: Board of Governors of the Federal Reserve System; modeled by fred.stlouisfed.org*)

Whether this has anything to do with commodity financialization is difficult to say. If we want to talk purely in terms of correlations, oil and the effective federal funds rate have had a -0.53 correlation coefficient on a quarterly interval since 1986. Between oil and the US dollar (NYSEARCA:UUP)(NYSEARCA:UDN), a well-known negative correlation, the coefficient comes to -0.49. Between the US dollar and federal funds rate, the correlation coefficient comes to 0.11.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.