Econbrowser readers will know that I’ve long been interested in how derivatives like futures predict commodity prices. An early paper on energy futures, coauthored with my former CEA colleagues Michael LeBlanc and Oli Coibion, was summarized in this 2006 post (paper here). Recently, Oli Cobion and I have updated and expanded our examination, to incorporate for the most recent data, account for GARCH effects, alloow for time variation, and to try to explain why there has been time variation in the deviations in the unbiasedness proposition.
From the abstract to our paper:
This paper examines the relationship between spot and futures prices for a broad range of commodities, including energy, precious and base metals, and agricultural commodities. In particular, we examine whether futures prices are (1) an unbiased and/or (2) accurate predictor of subsequent spot prices. While energy futures prices are generally unbiased predictors of future spot prices, there is much stronger evidence against the null for other commodity markets. This difference appears to be driven in part by the depth of each market. We find that over the last five years, it is much harder to reject the null of futures prices being unbiased predictors of future spot prices than in earlier periods for almost all commodities. In addition, futures prices do approximately as well as a random walk in forecasting future spot prices, and vastly outperform a reduced form empirical model.
The paper is also available as NBER Working Paper No. 15830.
The regression we run is:
st – st-k = β 0 + β 1 (f t|t-k – st-k) + ε t
Where st is the log spot price at time t, ft|t-k is the log futures price at time t-k that matures at time t. The resulting β coefficients at the three month horizons are displayed in Figure 1.
Figure 1: β1 coefficients, estimated via OLS. *** (**) denotes significantly different from unity at the 1% (5%) level, using HAC robust standard errors. Source: Chinn and Coibion (2010).
As Jim Hamilton has pointed out in a related context (e.g., Fed Funds futures)  [pdf], accounting for GARCH effects can be important, particularly when making inferences regarding unbiasedness. Hence, we re-estimate the equation to obtain the following coefficients:
Figure 2: β1 coefficients, estimated using GARCH. *** (**) denotes significantly different from unity at the 1% (5%) level. Source: Chinn and Coibion (2010).
What about what determines the deviation from the unbiasedness hypothesis? To assess whether there is a link between the depth of each market and how closely the no-arbitrage condition holds. Figure 15 plots the (log) average monthly volume of trades for each type of commodity (averaged across 3-month and 6-month futures) from 2006-2009 versus the average absolute value of the t-statistic for the null of unbiasedness for 3-month and 6-month futures for each commodity type. There is a clear negative correlation. Market depth appears empirically important.
Figure 3: Average of the absolute value of the t-statistics for the null of unbiasedness for 3-month and 6-month futures for each commodity against average monthly trading volume, in logs, between 2006 and 2009. See empirical estimates of Table 1 in the paper. Source: Chinn and Coibion (2010).
Finally, just so readers can see what the variables in question look like, I present a plot of what the basis at 3 and 6 months look like for oil, since the price of petroleum is perennially of interest.
Figure 4: Price of Petroleum, WTI, end of month (blue, left axis), and the log 3 (solid, right axis) and 6 (dashed, right axis) month basis. Source: Chinn and Coibion (2010).
By the way, our tests of unbiasedness — and corresponding results that fail to reject that hypothesis — should not be taken as implying that futures are always correct; just that they are on average correct. For one (historical) case where the futures pointed in the wrong direction, see J. Hamilton, “Was the Deflation During the Great Depression Anticipated? Evidence from the Commodity Futures Market” AER 1992.