In this paper we present an equilibrium model of commodity spot (s t ) and futures (f t ) prices, with finite elasticity of arbitrage services and convenience yields. By explicitly incorporating and modelling endogenously the convenience yield, our theoretical model is able to capture the existence of backwardation or contango in the long-run spot-futures equilibrium relationship, s t = β 2 f t + β 3 . When the slope of the cointegrating vector b 2 > 1 (b 2 < 1) the market is under long run backwardation (contango). It is the first time in this literature in which the theoretical possibility of finding a cointegrating vector different from the standard b 2 =1 is formally considered.Independent of the value of b 2 , this paper shows that the equilibrium model admits an economically meaningful Error Correction Representation, where the linear combination of (s t ) and (f t ) characterizing the price discovery process in the framework of Garbade and Silber (1983), coincides exactly with the permanent component of the Gonzalo-Granger (1995) PermanentTransitory decomposition. This linear combination depends on the elasticity of arbitrage services and is determined by the relative liquidity traded in the spot and futures markets. Such outcome not only provides a theoretical justification for this Permanent-Transitory decomposition; but it offers a simple way of detecting which of the two prices is dominant in the price discovery process. All the results are testable, as it can be seen in the application to spot and futures non-ferrous metals prices (Al, Cu, Ni, Pb, Zn) traded in the London Metal Exchange (LME). Most markets are in backwardation and futures prices are "information dominant" in highly liquid futures markets (Al, Cu, Ni, Zn).JEL classification: C32, C51, G13, G14.

This paper applies the mildly explosive/multiple bubbles testing methodology developed by Phillips, Shi and Yu (2015a, International Economic Review, forthcoming) to examine the recent time series behaviour of the main six London Metal Exchange (LME) non-ferrous metals prices. We detect periods of mild explosivity in the cash and three-month futures price series in each of copper, nickel, lead, zinc and tin, but not in aluminium. We argue that convenience yield, though the formal counterpart to dividend yield in commodity markets, is not a useful basis on which to assess whether observed explosivity is indicative of bubbles (namely, departures of prices from their fundamental values). We construct other measures that provide evidence that suggests the observed explosivity in the non-ferrous metals market can be associated with tight physical markets.

We analyze the price behaviour of the main precious metals -gold, silver, platinum and palladium -before, during and in the aftermath of the 2007-08 financial crisis. Using the mildly explosive/multiple bubbles technology developed by Phillips, Shi and Yu (2015, International Economic Review 56(4), 1043-1133), we find significant, short periods of mildly explosive behaviour in the spot and futures prices of all four metals. Fewer periods are detected using exchange-rate adjusted prices, and almost none when deflated prices are used.We assess whether these findings are indicative of bubble behaviour. Convenience yield is shown to have little efficacy in this regard, while other fundamentals proxy variables and position data offer only very limited evidence against prices having been anything other than fundamentals-driven. Possible exceptions are in gold in the run-up to the highpoint of the financial crisis, and in silver and palladium around the launch of specific financial products. Some froth, however, is reported and discussed for each metal.JEL classification: C22; D84; G13

This paper provides an analysis of oil prices during and in the aftermath of the Global Financial Crisis, concentrating on the 2007-08 price spike and the 2014-16 price decline. The mildly explosive/multiple bubbles testing strategy by Phillips, Shi and Yu (2015, International Economic Review 56(4), 1043-1133) is used to test for price departures from an underlying stochastic trend and to assess whether any such departures can be explained by fundamentals or other proxy variables. The test dates two significant time periods in both Brent and WTI nominal and real front-month futures prices: a mildly explosive episode during the 2007-08 spike, prior to the peak of the Global Financial Crisis; and a significantly shorter, negative such episode during the 2014-16 price decline, whose commencement is dated around a key OPEC meeting in November 2014. Evidence using other commodity prices points to explanatory factors beyond commodity markets. A global economic activity proxy is found to be decisive in the episode in mid-2008; excess speculation is not. U.S. shale oil production, though contributing to the post-June 2014 price decline, is not seen to have been decisive. Against some recent work tying the CBOE Volatility Index (VIX) to oil futures prices, we find no evidence that the VIX decisively affected oil price levels during the sample period. The results are compared and contrasted with those obtained by Baumeister and Kilian (2016, Journal of the Association of Environmental and Resource Economists 3, 131-158) via a forecasting approach based on a structural vector autoregressive model without financial variables. Taken altogether, the results herein provide new evidence based on formal statistical testing that help resolve a number of recent controversies in the oil price literature.