2064 The Journal of Finance R
aggregation among market participants and helps them overcome the informational
frictions they face (e.g., Grossman and Stiglitz (1980) and Hellwig
(1980)). This framework, however, crucially relies on the combination of constant
absolute risk aversion (CARA) utility functions for agents and Gaussian
distributions for asset prices to ensure a tractable linear equilibrium, and thus
one cannot readily adopt this framework to analyze commodity markets, in
which both CARA utility and Gaussian distributions are unrealistic. It is challenging
to analyze information aggregation in settings without the tractable
linear equilibrium. This technical challenge is common in analyzing how asset
prices affect real activity, such as firm investment and central bank policies,
through an informational channel.2
In this paper, we aim to confront this challenge by developing a tractable
model to analyze how informational frictions affect commodity markets. Our
model integrates the standard framework of asset market trading with asymmetric
information into an international macro setting (e.g., Obstfeld and
Rogoff (1996) and Angeletos and La’O (2013)). In this global economy, a continuum
of specialized goods producers whose production has complementarity—
which emerges from their need to trade produced goods with each other—
demand a key commodity, such as copper, as a common production input.
Through trading the commodity, the goods producers aggregate dispersed information
regarding unobservable global economic strength, which ultimately
determines their commodity demand.
Our main model focuses on a centralized spot market through which the
goods producers acquire the commodity from a group of suppliers, who are subject
to an unobservable supply shock. The supply shock prevents the commodity
price from perfectly aggregating the goods producers’ information with respect
to the strength of the global economy. Nevertheless, the commodity price provides
a useful signal to guide the producers’ production decisions and commodity
demand. Despite the nonlinearity in the producers’ production decisions, we
derive a unique log-linear equilibrium in closed form. In this equilibrium, each
producer’s commodity demand is a log-linear function of its private signal and
the commodity price, while the commodity price is a log-linear function of global
economic strength and the supply shock. This tractable log-linear equilibrium
builds on a combination of Cobb-Douglas utility functions for households, lognormal
distributions for commodity prices, and a key aggregation property: the
aggregate demand of a continuum of producers remains log-linear as a result of
the Law of Large Numbers. We also extend the model to incorporate a futures
market to further characterize the role of futures market trading.
It is common for empirical studies of commodity markets to rely on conventional
wisdom generated from settings without any informational frictions
(i.e., agents directly observing both supply and demand shocks). According to
such wisdom, (1) a higher price leads to lower commodity demand as a result
of the standard cost effect, (2) a positive supply shock reduces the commodity
price, which in turn stimulates greater commodity demand, and (3) the futures
2 See a recent review by Bond, Edmans, and Goldstein (2012).