Interest Rate Dynamics and Commodity Prices

Abstract

In economic studies and popular media, interest rates are routinely cited as a major factor behind commodity price fluctuations. At the same time, the transmission channels are far from transparent, leading to long-running debates on the sign and magnitude of interest rate effects. Purely empirical studies struggle to address these issues because of the complex interactions between interest rates, prices, supply changes, and aggregate demand. To move this debate to a solid footing, we extend the competitive storage model to include stochastically evolving interest rates. We establish general conditions for existence and uniqueness of solutions and provide a systematic theoretical and quantitative analysis of the interactions between interest rates and prices.

Figures (6)

• Figure 1: The real interest rate over the long run (one-year US treasury yield deflated by a measure of expected inflation obtained from an autoregressive model estimated on a 30-year rolling window). Source: FRED.
• Figure 2: Illustration of the equilibrium price function $f^*$ and the equilibrium storage rule $i^*$. $p$ represents the inverse demand function, $\bar{p}$ denotes the price threshold at which speculators begin holding inventories, and $x^*$ is the threshold for free disposal.
• Figure 3: $\kappa(M)$ values for different combinations of $(\mu_R, \rho_R, \sigma_R)$. The parameter $\kappa(M)$ represents the asymptotic yield on risk-free zero-coupon bonds as maturity approaches infinity, with $(\mu_R, \rho_R, \sigma_R)$ controlling the dynamics of the gross real interest rate process. In the left panel, $\rho_R$ is fixed at its estimated value, and a contour plot of $\kappa(M)$ is provided as a function of $(\mu_R, \sigma_R)$. In the right panel, $\sigma_R$ is fixed at its estimated value, and a contour plot of $\kappa(M)$ is shown as a function of $(\mu_R, \rho_R)$.
• Figure 4: IRFs for a 100 bp real interest rate shock under different parameter setups without demand channel, fixing $X_{t-1}$ and $R_{t-1}^a$ at the stationary mean. $X_{t-1}$ and $R_{t-1}^a$ are the total available supply and the annual gross real interest rate in the previous quarter, $\delta$ is the rate of depreciation, and $\lambda$ is the demand elasticity.
• Figure 5: IRFs for a 100 bp real interest rate shock conditional on different states without demand channel. $(X_{t-1}^p, R_{t-1}^{a,p})$ denotes the percentile points of the realized total available supply and interest rate states on the stationary distribution, and $\mu_R$ and $\bar{X}$ are the stationary means of the interest rate and the total available supply processes, respectively.

Theorems & Definitions (59)

• Example 2.1
• Theorem 2.1: Existence and Uniqueness of Equilibrium Price
• Proposition 2.1: Existence and Uniqueness of Equilibrium Storage
• Proposition 3.1: Monotonicity of Equilibrium Objects w.r.t. the Exogenous State
• Example 3.1
• Example 3.2
• Example 3.3
• Proposition 3.2: Negative Correlation of Interest Rates and Prices
• Remark 3.1
• Example 3.4