Inflation Hedging Potential of Commodity Indices and Futures for U.S. Investors

Abstract

This study provides a comprehensive examination of the inflation-hedging potential of commodity indices and futures for U.S. investors using monthly data spanning July 1959 to December 2025 for 27 individual commodities, and January 1947 to November 2025 for 13 commodity indices. We employ multiple complementary methodologies, including optimal hedge ratios with Newey–West standard errors, asymmetric hedging analysis, long-horizon regressions, rolling window stability tests, Granger causality analysis, out-of-sample validation, and Markov-switching vector error correction models (MS-VECM). Our results reveal substantial heterogeneity in hedging effectiveness across commodity sectors. Energy commodities, particularly gasoline and crude oil, demonstrate the strongest inflation-hedging properties with higher hedge ratios and hedging effectiveness. Industrial metals, represented by copper, also provide reliable hedging with stable performance across market conditions. In contrast, precious metals, including gold and silver, show weak contemporaneous hedging ability despite their traditional safe-haven reputation, though they may offer protection during specific market regimes. Agricultural commodities and livestock exhibit minimal or negative hedging effectiveness. The MS-VECM analysis confirms that hedging relationships are time-varying, with effectiveness differing significantly between stable and turbulent market regimes. These findings have important implications for portfolio construction and risk management strategies.

1. Introduction

The inflation-hedging capacity of financial assets has re-emerged as a central concern amid the recent resurgence of inflationary pressures. U.S. CPI inflation increased sharply to 7% in 2021 before moderating to 6.5% in 2022, 3.4% in 2023, and 2.9% in 2024, underscoring both the persistence and unpredictability of inflation dynamics. This environment has renewed investor and institutional interest in assets capable of preserving real purchasing power across varying macroeconomic conditions. Among alternative asset classes, commodities occupy a distinctive role because their prices are intrinsically linked to the production and consumption processes of the real economy. Unlike traditional financial assets, whose real returns may deteriorate during inflationary episodes, commodity prices often adjust contemporaneously with changes in the general price level. Consequently, commodity futures and commodity indices have become central instruments in inflation-hedging strategies and portfolio risk management.

The academic literature on commodity inflation hedging has evolved considerably over time. Earlier studies primarily focused on whether commodities, as a broad asset class, protect against inflation through positive contemporaneous correlations with consumer prices. Subsequent research expanded this perspective by examining sectoral heterogeneity, regime dependence, time variation, and dynamic transmission mechanisms. More recent studies increasingly emphasize that inflation-hedging effectiveness differs substantially across commodity sectors, macroeconomic environments, investment horizons, and econometric methodologies. Despite these advances, the literature continues to present conflicting conclusions regarding which commodities provide reliable inflation protection and under what economic conditions such protection materializes.

This study reexamines the inflation-hedging potential of commodity futures and commodity indices from a U.S. investor perspective using one of the most comprehensive datasets assembled in the literature. Specifically, we analyze 27 individual commodity futures from July 1959 to December 2025 and 13 commodity indices from January 1947 to November 2025, thereby encompassing multiple complete inflation cycles, including the Great Inflation of the 1970s, the Great Moderation, the Global Financial Crisis, and the recent post-pandemic inflation surge. In contrast to studies focusing on limited commodity subsets or shorter sample windows, this framework allows for a unified evaluation of commodity inflation hedging across structurally distinct macroeconomic regimes.

To capture the multidimensional nature of commodity–inflation relationships, we employ an integrated empirical framework combining both static and dynamic methodologies. Our analysis includes optimal hedge ratio estimation using OLS with Newey–West heteroskedasticity and autocorrelation consistent standard errors, asymmetric hedging analysis, multi-horizon analysis across 1- to 36-month investment horizons, rolling-window stability analysis, Granger causality tests, out-of-sample validation with 70/30 splits, regime-dependent analysis across inflation environments, and Markov-Switching Vector Error Correction Models (MS-VECM) following Liu et al. (2023). This multi-methodological structure enables us to evaluate not only whether commodities hedge inflation, but also whether such relationships remain stable across time, investment horizons, and inflationary environments.

The empirical findings reveal substantial heterogeneity in inflation-hedging effectiveness across commodity sectors. Energy commodities exhibit the strongest and most stable inflation-hedging properties throughout nearly all specifications. Energy commodities exhibit the strongest inflation-hedging properties because energy prices represent a core input cost across nearly all sectors of the economy, including transportation, manufacturing, and utilities. Consequently, inflationary pressures are accompanied by contemporaneous increases in energy prices through broad cost pass-through and demand-driven transmission mechanisms. In addition, major inflationary episodes were closely linked to disruptions in global energy markets. As a result, energy commodities generally demonstrate stronger and more stable inflation sensitivities than other commodities. Gasoline RBOB and crude oil WTI display exceptionally large hedge ratios and high hedging effectiveness, indicating strong contemporaneous sensitivity to realized inflation. Industrial metals, particularly copper, also provide meaningful inflation protection under certain conditions. The relationship between inflation and copper prices arises from copper’s central role in industrial production, construction, and infrastructure. Inflationary periods increase industrial demand and production costs, placing upward pressure on copper prices through both demand- and cost-driven channels. In addition, copper prices rapidly incorporate expectations regarding economic growth and future inflation, making copper a forward-looking indicator of inflationary dynamics. In contrast, precious metals such as gold and silver demonstrate surprisingly weak contemporaneous hedging ability despite their conventional reputation as inflation hedges, although dynamic regime-dependent analysis suggests that they may protect during extreme inflationary periods. Agricultural commodities and livestock generally exhibit weak, unstable, or insignificant hedging effectiveness.

The MS-VECM analysis further demonstrates that commodity inflation-hedging relationships are highly time-varying and regime dependent. Several commodities display markedly different adjustment dynamics during stable versus turbulent inflationary environments, implying that static hedge ratios may inadequately capture true hedging performance. Moreover, the results suggest that inflation hedging in commodity markets operates primarily through contemporaneous price transmission mechanisms rather than long-run equilibrium correction.

This paper contributes to the literature in several dimensions. First, we provide one of the most comprehensive empirical examinations to date, with an extended sample spanning nearly eight decades for indices and over six decades for individual commodities. Second, our multi-methodological framework reconciles conflicting findings in prior studies by demonstrating how different approaches capture different dimensions of the hedging relationship. Third, we provide definitive evidence on the energy versus precious metals debate, documenting that energy commodities are the only reliable inflation hedges while gold fails to provide systematic protection. Fourth, we document substantial asymmetric effects and within-sector heterogeneity that have practical portfolio implications. Finally, the MS-VECM analysis advances understanding of the mechanism through which commodity hedging operates.

These findings carry important implications for institutional portfolio management, inflation-risk mitigation, and strategic asset allocation. The evidence suggests that broad commodity exposure alone may not provide reliable inflation protection. Instead, effective inflation hedging requires sector-specific allocation, active monitoring of macroeconomic regimes, and dynamic portfolio adjustment. In particular, the results indicate that energy-based commodity exposure constitutes the dominant source of inflation protection within commodity markets, while static allocations to precious metals or broad commodity baskets may overstate long-run hedging effectiveness.

The remainder of this paper is organized as follows. Section 2 reviews the related literature. Section 3 describes our data and methodology. Section 4 presents empirical results. Section 5 discusses economic interpretations and implications. Section 6 concludes this paper.

2. Literature Review

The literature examining the inflation-hedging properties of commodities has expanded substantially over the past several decades, yet the empirical evidence remains fragmented and often inconclusive. Early studies generally treated commodities as a broad asset class and focused primarily on whether commodity prices maintain positive contemporaneous relationships with inflation. Becker and Finnerty (2000) and Gorton and Rouwenhorst (2006) argue that commodity futures provide diversification benefits and preserve purchasing power during inflationary periods because commodity prices are directly tied to production costs and real economic activity. Similarly, Spierdijk and Umar (2014) document that commodity futures exhibit inflation-hedging potential over longer investment horizons, particularly within energy and industrial metals markets. Zaremba et al. (2019), employing several centuries of historical data, further conclude that broad commodity exposure may protect prolonged inflationary regimes.

Despite this broad consensus, the literature increasingly recognizes that commodity inflation hedging is neither uniform nor stable across sectors, market conditions, or investment horizons. A growing body of research documents substantial heterogeneity across commodity groups. Belousova and Dorfleitner (2012) demonstrate that commodity markets exhibit distinct cross-sectional return and diversification characteristics, implying that inflation sensitivity should differ meaningfully across individual commodities. More recent studies reinforce this argument. Rubbaniy et al. (2022) show that soft commodities display highly heterogeneous hedging behavior across investment horizons, while Futerman and Sarjanovic (2022) distinguish between storable and non-storable commodities and report materially different inflation sensitivities between the two categories. Collectively, this literature suggests that treating commodities as a homogeneous inflation-hedging asset class may obscure substantial within-sector variation.

The literature also increasingly emphasizes the importance of regime dependence and time variation in commodity-inflation relationships. Brière and Signori (2012) argue that inflation-hedging effectiveness varies significantly across macroeconomic environments, particularly during periods of elevated uncertainty and inflation volatility. Liu et al. (2023), using a Markov-Switching Vector Error Correction Model (MS-VECM), demonstrate that commodity futures exhibit materially different hedging properties across inflation-dominated and stable economic regimes. Similarly, Valadkhani and O’Mahony (2024) show that precious metals hedge inflation more effectively during high-inflation periods than during normal market environments. These findings challenge earlier static approaches by suggesting that inflation-hedging relationships evolve over time and may strengthen or weaken depending on prevailing macroeconomic conditions.

At the same time, the literature presents conflicting evidence regarding which commodities provide the most reliable inflation protection. Precious metals, particularly gold, have traditionally been viewed as canonical inflation hedges. Studies such as Jaiswal and Uchil (2015) and Salisu et al. (2020) report that gold and silver can preserve purchasing power under certain conditions. However, more recent evidence questions the consistency and stability of these relationships. D. G. Baur and Lucey (2010) argue that gold behaves more as a safe-haven asset during financial stress than as a direct inflation hedge, while Valadkhani et al. (2022) demonstrate that gold’s inflation-hedging ability is highly conditional on inflation regimes. Recent work by D. Baur (2025) and Fandetti (2024) further emphasizes the instability of gold’s relationship with inflation over time. In contrast, studies focusing on energy commodities often report stronger and more consistent inflation sensitivity because energy prices directly affect transportation, production, and consumer prices throughout the economy. Nevertheless, the magnitude and persistence of energy-based inflation hedging remain insufficiently explored across multiple inflation cycles and econometric specifications.

Another important theme within the literature concerns methodological fragmentation. The traditional optimal hedge ratio framework developed by Ederington (1979) remains widely employed because of its intuitive interpretation and simplicity. However, static ordinary least squares approaches assume stable relationships and therefore may fail to capture structural breaks, asymmetric responses, or regime shifts. To address these limitations, subsequent studies introduced alternative econometric frameworks. Hadad et al. (2024) adopt time-varying parameter models to demonstrate that commodity hedging effectiveness changes substantially during periods of market stress. Liu et al. (2023) extend this literature through MS-VECM estimation, highlighting the importance of nonlinear adjustment dynamics across macroeconomic regimes. Although these approaches advance the literature, most existing studies rely on a single methodological framework, making it difficult to determine whether conflicting conclusions reflect genuine economic differences or methodological sensitivity.

Relatedly, a growing stream of research suggests that commodity inflation hedging may be asymmetric. Existing studies often assume that commodities respond symmetrically to inflationary and disinflationary shocks. However, recent evidence suggests otherwise. Adekoya et al. (2023) demonstrate that industrial metals exhibit stronger inflation-hedging performance when asymmetric modeling techniques are employed, whereas Ouyang et al. (2024) document the asymmetric macroeconomic effects of commodity shocks. Valadkhani and O’Mahony (2024) similarly report that precious metals provide stronger protection specifically during high-inflation episodes. Nevertheless, explicit tests distinguishing inflationary from disinflationary hedging dynamics remain relatively uncommon in the commodity literature.

Despite substantial progress, several important gaps remain unresolved. First, much of the existing literature relies on relatively narrow commodity subsets, short sample periods, or aggregate commodity classifications, limiting the ability to evaluate inflation-hedging performance across structurally distinct macroeconomic environments. Many studies exclude either the Great Inflation of the 1970s or the recent post-pandemic inflation surge, thereby reducing the generalizability of their conclusions across multiple inflation cycles. Second, the literature has yet to establish a unified framework capable of reconciling conflicting findings regarding the relative effectiveness of energy commodities, industrial metals, precious metals, and agricultural commodities. Third, prior studies frequently rely on a single econometric methodology, leaving unresolved whether differences in empirical findings stem from economic fundamentals or methodological design. Fourth, relatively limited attention has been devoted to asymmetric hedging behavior, rolling stability, out-of-sample validation, and within-sector heterogeneity across individual commodities.

This study addresses these limitations through a comprehensive empirical framework integrating extensive historical coverage, broad commodity representation, and multiple complementary methodologies within a unified structure. Specifically, the analysis examines 13 commodity indices from 1947 to 2025 and 27 individual commodity futures from 1959 to 2025, encompassing multiple inflationary regimes, including the Great Inflation, the Great Moderation, the Global Financial Crisis, and the post-pandemic inflation surge. In contrast to prior studies that rely on a single estimation approach, this study combines optimal hedge ratio estimation, asymmetric hedging analysis, multi-horizon regressions, rolling-window stability tests, Granger causality analysis, out-of-sample validation, regime-dependent estimation, and MS-VECM analysis. This integrated framework allows this study not only to evaluate whether commodities hedge inflation but also to identify how hedging effectiveness varies across sectors, investment horizons, inflation regimes, and econometric specifications.

3. Data and Methodology

We analyze two comprehensive datasets of commodity prices and returns. The first dataset contains monthly price levels for 13 commodity indices from January 1947 to November 2025. These commodity index data are obtained from the Commodity Research Bureau (CRB). The CRB indices include seven sub-indices: Metals, Textiles, Raw Industrials, Foodstuffs, Fats and Oils, Livestock, and the CRB Spot Index. Additionally, we include six S&P GSCI sub-indices: Agricultural, Energy, Industrial Metals, Livestock, Precious Metals, and the composite S&P GSCI Index. The CRB indices have complete data from 1947, while the GSCI indices begin at various dates between 1969 and 1983, depending on the sub-index.

The second dataset contains monthly returns for 27 individual commodity futures, starting at different dates from July 1959 to December 2025 (Please see Appendix A for details on the starting date for each index and commodity). These commodities span eight sectors: Energy (Gasoline RBOB, Crude Oil WTI, ULSD NY Harbor, Natural Gas), Precious Metals (Gold, Silver, Platinum, Palladium), Industrial Metals (Copper), Grains (Corn, Wheat, Oats, Rough Rice), Oilseeds (Soybean, Soybean Oil, Soybean Meal, Canola), Softs (Coffee, Cocoa, Sugar #11, Cotton #2, Orange Juice), Livestock (Live Cattle, Feeder Cattle, Lean Hogs), and Other (Lumber, Class III Milk). Sample sizes vary by commodity due to data availability, ranging from 306 observations for Class III Milk to 798 observations for commodities with complete data.

For our measure of inflation, we use the Consumer Price Index (CPI) for All Urban Consumers from the Bureau of Labor Statistics. We compute monthly log returns as the first difference in the natural logarithm of the CPI price level, multiplied by 100 to express values as percentages. This approach provides a continuous, percentage-based measure of monthly inflation that is comparable to commodity returns.

We employ multiple complementary methodologies to provide a comprehensive assessment of inflation-hedging properties. First, our primary measure is the optimal hedge ratio following Ederington (1979):

h* = Cov(r, π)/Var(π) = β from OLS regression,

where r represents commodity returns and π represents inflation.

The hedge ratio indicates the position size needed to hedge one unit of inflation exposure. We estimate hedge ratios using OLS regression with Newey–West heteroskedasticity and autocorrelation consistent (HAC) standard errors with four lags to account for serial correlation in the residuals.

Hedging effectiveness measures variance reduction and equals the R-squared from the regression:

HE = 1 − Var(hedged)/Var(unhedged) = R²

Second, for the asymmetric hedging analysis, we separate inflation into positive and negative components to test whether commodities hedge inflation increases and decreases equally:

$$r_t=\mathsf{\alpha }+{\mathsf{\beta }}^{+}\times \mathrm{m}\mathrm{a}\mathrm{x}({\pi }_t,0)+{\mathsf{\beta }}^{-}\times \mathrm{m}\mathrm{i}\mathrm{n}({\pi }_t,0)+{\epsilon }_t$$

We test for asymmetry using a t-test of the null hypothesis that β⁺ = β⁻, with standard errors computed using the Newey–West covariance matrix.

Third, multi-horizon analysis examines hedge ratios across investment horizons from 1 to 36 months using cumulative returns. For horizon h, we compute cumulative commodity returns and cumulative inflation over h months and estimate the hedge ratio from their regression. This analysis reveals whether hedging effectiveness improves or deteriorates over longer investment periods.

Fourth, rolling window estimation uses 60-month windows to assess hedge ratio stability over time, as well as computing statistics, including mean, standard deviation, minimum, maximum, and percentage of windows with positive hedge ratios. We select a 60-month window for three reasons: (1) it provides sufficient observations for reliable OLS estimation while capturing a complete business cycle; (2) it aligns with standard practice in the literature (Erb & Harvey, 2006; Gorton & Rouwenhorst, 2006); (3) it balances responsiveness to structural changes against estimation noise from shorter windows. We report the mean, standard deviation, and percentage of windows with positive hedge ratios.

Fifth, Granger causality tests examine predictive relationships using an F-test comparing restricted and unrestricted models with four lags. This determines whether past inflation helps predict commodity returns (inflation Granger-causes commodity) or vice versa (commodity Granger-causes inflation).

Sixth, out-of-sample validation uses a 70/30 split, estimating hedge ratios on the first 70% of observations and testing hedging effectiveness on the remaining 30%. We classify performance as stable if the absolute difference between in-sample and out-of-sample hedging effectiveness is less than 15 percentage points.

Seventh, regime-dependent analysis examines hedge ratios across four inflation environments based on trailing 12-month inflation: Disinflation (below 0%), Moderate (0–3%), High (3–6%), and Very High (above 6%).

Finally, we employ Markov-Switching Vector Error Correction Models (MS-VECM) following Liu et al. (2023). We identify two regimes based on 24-month rolling volatility: Regime 1 (stable/low volatility) and Regime 2 (turbulent/high volatility). This approach identifies distinct market regimes based on volatility clustering and estimates separate VECM parameters for each regime. The error correction coefficient indicates the speed of adjustment to long-run equilibrium, with positive and significant coefficients on the commodity equation indicating inflation-hedging ability.

4. Empirical Results

4.1. Optimal Hedge Ratios

Table 1 reports optimal hedge ratios estimated from OLS regressions of commodity returns on CPI inflation, with Newey–West corrections. The hedge ratio measures contemporaneous inflation sensitivity, while hedging effectiveness (HE) captures the fraction of inflation variance explained by commodity returns.

Table 1. Optimal hedge ratios.

Panel A: Commodity Indices
Index	Hedge Ratio	t-Stat	HE (%)	N
CRB Metals	2.70 **	2.39	4.04	946
CRB Textiles	1.44 ***	3.92	3.10	946
CRB Raw Industrials	2.15 ***	3.39	6.66	946
CRB Foodstuffs	3.02 ***	5.54	7.53	946
CRB Fats and Oils	3.99 ***	4.20	4.55	946
CRB Livestock	3.29 ***	4.01	4.54	946
CRB Spot Index	2.48 ***	4.57	10.02	946
GSCI Agricultural	3.69 ***	3.54	4.25	671
GSCI Energy	20.77 ***	10.36	34.85	515
GSCI Industrial Metals	3.11 **	2.10	2.41	587
GSCI Livestock	0.84	1.13	0.26	670
GSCI Precious Metals	2.60 **	2.21	2.17	632
S&P GSCI Index	7.69 ***	6.25	18.31	671
Panel B: Individual Commodity Futures
Commodity	Hedge Ratio	t-Stat	HE (%)	N
Gasoline RBOB	25.72 ***	10.41	43.25	492
Crude Oil WTI	21.93 ***	8.07	31.68	513
ULSD NY Harbor	13.72 ***	5.88	22.59	565
Natural Gas	13.56 ***	4.77	6.57	428
Gold	1.32	1.23	0.62	611
Silver	2.59	1.32	0.78	750
Platinum	2.44	1.54	0.79	693
Palladium	1.81	0.89	0.29	587
Copper	2.43	1.37	0.95	797
Corn	3.67 ***	2.94	2.84	797
Wheat	2.34 *	1.89	0.99	797
Oats	2.29	1.50	0.71	797
Rough Rice	2.19	1.21	0.55	426
Soybean	1.27	1.10	0.31	797
Soybean Oil	5.03 ***	3.04	3.55	797
Soybean Meal	−0.35	−0.28	0.02	797
Canola	0.74	0.77	0.13	611
Coffee	2.17 *	1.89	0.50	640
Cocoa	3.19 ***	2.86	1.21	797
Sugar #11	3.88 **	2.08	1.17	779
Cotton #2	2.52 **	2.25	1.23	797
Orange Juice	2.47 *	1.75	0.71	706
Live Cattle	0.15	0.17	0.01	649
Feeder Cattle	−0.17	−0.18	0.01	628
Lean Hogs	0.94	0.85	0.14	717
Lumber	1.93	1.57	0.39	668
Class III Milk	2.64 ***	3.25	3.37	305

This table reports optimal hedge ratios estimated from OLS regressions of commodity returns on CPI inflation. Panel A presents results for 13 commodity indices; Panel B presents results for 27 individual commodity futures. Hedge Ratio is the slope coefficient (β) from the regression $r_t=\mathsf{\alpha }+{\mathsf{\beta }}^{+}\times \mathrm{m}\mathrm{a}\mathrm{x}({\pi }_t,0)+{\mathsf{\beta }}^{-}\times \mathrm{m}\mathrm{i}\mathrm{n}({\pi }_t,0)+{\epsilon }_t$. t-Stat is computed using Newey-West heteroskedasticity and autocorrelation consistent standard errors with 4 lags. HE (%) is hedging effectiveness measured by R-squared, representing the percentage of commodity return variance explained by inflation. N is the number of monthly observations. Statistical significance is denoted by *** (p < 0.01), ** (p < 0.05), and * (p < 0.10).

The index-level results reveal substantial sectoral heterogeneity. The GSCI Energy index exhibits the largest and most precisely estimated hedge ratio (20.77) and the highest hedging effectiveness (34.85%). This magnitude indicates strong contemporaneous co-movement between energy prices and realized inflation, consistent with the direct inclusion of energy components in the CPI basket. The broad S&P GSCI index also displays economically meaningful inflation sensitivity (7.69; HE = 18.31%), largely reflecting its energy weighting.

CRB sub-indices show positive and statistically significant hedge ratios in the range of 2–4. Although smaller than those of energy-focused indices, these coefficients remain economically relevant and suggest partial inflation protection through diversified commodity exposure. The CRB Spot Index exhibits relatively stable hedging effectiveness exceeding 10%. In contrast, the GSCI Livestock index shows no statistically significant relationship with inflation, indicating limited macro-level price linkage in that sector. Overall, inflation hedging at the index level is concentrated in energy markets. Broader indices provide positive but more moderate exposure, and their effectiveness depends critically on sectoral composition.

Disaggregation into individual futures contracts reinforces and sharpens these patterns: Energy contracts dominate. Gasoline RBOB (25.72; HE = 43.25%) and Crude Oil WTI (21.93; HE = 31.68%) display large, highly significant coefficients, indicating strong and economically meaningful responsiveness to inflation shocks. ULSD and Natural Gas also show positive and significant hedge ratios, although natural gas exhibits lower explanatory power, reflecting greater idiosyncratic volatility.

Several agricultural and soft commodities, such as Soybean Oil, Corn, Cocoa, Sugar #11, and Class III Milk, demonstrate statistically significant but moderate inflation sensitivity. While these commodities co-move with inflation, their hedging effectiveness remains limited relative to energy contracts, suggesting that supply-side dynamics dilute their macroeconomic linkage. By contrast, precious metals, including gold and silver, exhibit weak and statistically insignificant contemporaneous hedge ratios. The low explanatory power indicates that realized CPI inflation does not systematically drive their returns in the static framework. This evidence does not support the characterization of precious metals as reliable direct hedges against realized inflation over the sample period. Livestock futures and several grain contracts display negligible or insignificant coefficients, further highlighting that commodity inflation hedging is not uniform across sectors.

Table 1 indicates that inflation sensitivity within commodity markets is highly concentrated rather than broad-based. Effective hedging appears driven primarily by energy exposure, with limited support for generalized commodity allocation as a uniform inflation protection strategy. These results highlight the importance of sector-level selection in inflation-hedging portfolios.

The results in Table 1 refine the prevailing view in the literature by demonstrating that inflation-hedging effectiveness is highly concentrated within the energy sector rather than broadly distributed across commodities. While prior studies, such as Gorton and Rouwenhorst (2006), Becker and Finnerty (2000), and Futerman and Sarjanovic (2022), support the role of commodities as inflation hedges, our findings suggest that such conclusions are largely driven by energy-related exposures. In contrast to the conventional emphasis on gold and other precious metals, the evidence in Table 1 aligns more closely with Belousova and Dorfleitner (2012), Zhang et al. (2019), and Hadad et al. (2024), who stress cross-commodity heterogeneity. Relative to Liu et al. (2023), which identify stronger hedging properties in metals under certain regimes, the broader U.S. sample in this research suggests that energy-based commodities provide more consistent contemporaneous protection against inflation.

4.2. Asymmetric Hedging Effects

Table 2 examines whether commodity returns respond symmetrically to positive and negative inflation shocks. The evidence suggests that inflation hedging is often asymmetric, with economically significant implications.

Table 2. Asymmetric hedging analysis.

Panel A: Commodity Indices
Index	Beta (Infl Up)	Beta (Infl Down)	Difference	Asymmetric?
CRB Metals	0.90	11.47	−10.57	No
CRB Textiles	1.22	2.48	−1.26	No
CRB Raw Industrials	1.00	7.74	−6.74	Yes
CRB Foodstuffs	2.08	7.58	−5.50	Yes
CRB Fats and Oils	1.96	13.83	−11.87	Yes
CRB Livestock	1.51	11.95	−10.45	Yes
CRB Spot Index	1.43	7.59	−6.16	Yes
GSCI Agricultural	3.08	6.66	−3.58	No
GSCI Energy	19.18	24.39	−5.22	No
GSCI Industrial Metals	0.66	12.96	−12.30	Yes
GSCI Livestock	−0.09	5.40	−5.49	Yes
GSCI Precious Metals	2.48	3.19	−0.71	No
S&P GSCI Index	5.36	19.07	−13.71	Yes
Panel B: Individual Commodity Futures
Commodity	Beta (Infl Up)	Beta (Infl Down)	Difference	Asymmetric?
Gasoline RBOB	22.95	31.87	−8.92	No
Crude Oil WTI	19.09	28.38	−9.29	No
ULSD NY Harbor	11.42	22.46	−11.04	Yes
Natural Gas	14.68	11.16	3.53	No
Gold	0.92	2.98	−2.06	No
Silver	1.34	8.94	−7.60	No
Platinum	0.93	9.87	−8.94	Yes
Palladium	−0.10	9.53	−9.63	Yes
Copper	−0.35	17.05	−17.40	Yes
Corn	2.78	8.33	−5.54	No
Wheat	1.54	6.53	−4.99	No
Oats	0.43	12.07	−11.64	Yes
Rough Rice	−0.35	7.26	−7.61	No
Soybean	0.12	7.37	−7.26	Yes
Soybean Oil	3.75	11.77	−8.02	Yes
Soybean Meal	−1.34	4.85	−6.19	Yes
Canola	−0.15	4.50	−4.65	No
Coffee	1.73	4.30	−2.57	No
Cocoa	2.18	8.48	−6.30	Yes
Sugar #11	3.37	6.57	−3.20	No
Cotton #2	0.88	11.18	−10.30	Yes
Orange Juice	2.08	4.37	−2.29	No
Live Cattle	−0.88	5.39	−6.27	Yes
Feeder Cattle	−1.46	6.01	−7.47	Yes
Lean Hogs	−0.05	5.91	−5.97	Yes
Lumber	0.81	7.24	−6.42	No
Class III Milk	2.07	3.69	−1.62	No
Gasoline RBOB	22.95	31.87	−8.92	No

This table examines whether commodities respond differently to inflation increases versus decreases. Panel A presents results for commodity indices; Panel B presents results for individual commodity futures. The model separates inflation into positive (β⁺) and negative (β⁻) components. Beta (Infl Up) captures the return response to positive inflation shocks (rising prices), while Beta (Infl Down) captures the response to negative inflation (falling prices or disinflation). Difference is calculated as β⁺ minus β⁻. Significant asymmetry (indicated by ‘Yes’) at the 5% level suggests that static hedge ratios may overstate or understate protection depending on the direction of inflation movements.

In Panel A of Table 2, eight of thirteen indices exhibit statistically significant asymmetry. For most CRB indices and the S&P GSCI, the coefficient associated with disinflation exceeds that for positive inflation. This pattern suggests that commodity returns adjust more strongly during periods of falling or moderating inflation than during inflationary accelerations. The GSCI Energy index is an exception. Its response remains large and statistically symmetric, reinforcing its role as a direct inflation-sensitive asset. These results imply that static hedge ratios may overstate protection during rising inflation while understating exposure during disinflationary episodes.

The disaggregated results in Panel B of Table 2 further reveal substantial within-sector heterogeneity. Energy contracts such as gasoline and crude oil do not exhibit significant asymmetry, indicating stable inflation sensitivity regardless of inflation direction. On the contrary, industrial metals and several agricultural commodities, including copper, soybean oil, and livestock contracts, display pronounced asymmetry, with stronger responses to disinflation than to inflation. Precious metals show limited evidence of directional sensitivity, consistent with their weak contemporaneous hedge ratios documented earlier.

These findings contribute to the literature by clarifying why prior studies relying on symmetric regression frameworks often reach conflicting conclusions. Ignoring asymmetry may obscure economically relevant differences across regimes and commodities. From a practical perspective, investors employing commodities as inflation hedges should account for directional sensitivity. Strategies calibrated to average hedge ratios may provide less protection during inflationary surges than expected, particularly in sectors other than energy. Dynamic allocation and sector selection, therefore, appear essential for effective inflation risk management.

These findings extend Adekoya et al. (2023) by demonstrating that asymmetry is not confined to industrial metals but is also relevant across several agricultural and livestock commodities. This distinction is important, as symmetric specifications may obscure economically meaningful hedging relationships. In contrast, energy commodities exhibit relatively stable responses across regimes, reinforcing their role as more reliable hedging instruments.

4.3. Multi-Horizon Analysis

Table 3 reports hedge ratios estimated over cumulative horizons from 1 to 36 months, allowing assessment of whether inflation protection strengthens or dissipates over time. The results indicate that inflation hedging is predominantly a short-horizon phenomenon, particularly for energy.

Table 3. Hedge ratios across investment horizons.

Panel A: Commodity Indices
Index	1 m	3 m	6 m	12 m	24 m	36 m
CRB Textiles	1.44	1.58	1.48	1.22	0.97	0.95
CRB Raw Industrials	2.15	2.37	2.14	1.66	1.17	1.03
CRB Foodstuffs	3.02	2.91	2.51	2.02	1.49	1.14
CRB Fats and Oils	3.98	4.10	3.44	2.50	1.53	1.03
CRB Livestock	3.29	3.18	2.54	1.88	1.32	1.10
CRB Spot Index	2.48	2.58	2.28	1.80	1.30	1.08
GSCI Agricultural	2.43	2.12	2.04	1.79	1.58	1.26
GSCI Energy	6.63	5.26	3.54	2.00	1.03	0.52
GSCI Industrial Metals	1.68	1.70	1.48	0.90	0.68	0.55
GSCI Livestock	0.59	0.81	0.73	0.66	0.73	0.73
GSCI Precious Metals	1.75	1.83	2.01	2.26	2.46	2.54
S&P GSCI Index	5.04	4.19	3.17	2.17	1.61	1.24
CRB Textiles	1.44	1.58	1.48	1.22	0.97	0.95
Panel B: Individual Commodity Futures
Commodity	1 m	3 m	6 m	12 m	24 m	36 m
Gasoline RBOB	11.07	7.68	4.70	2.49	1.12	0.41
Crude Oil WTI	9.86	7.92	5.43	3.28	1.78	1.10
ULSD NY Harbor	9.74	7.82	5.68	3.77	2.37	1.61
Natural Gas	6.28	5.30	5.12	3.87	2.64	2.15
Gold	1.00	0.65	0.65	0.60	0.46	0.39
Silver	2.37	1.73	1.33	0.94	0.80	0.69
Platinum	2.10	1.47	0.79	0.44	0.30	0.28
Palladium	1.23	0.88	0.59	−0.04	−0.50	−0.67
Copper	2.41	2.10	1.47	0.41	−0.26	−0.72
Corn	3.67	3.07	2.94	2.51	1.95	1.22
Wheat	2.35	1.85	1.92	1.94	1.60	1.23
Oats	2.29	1.69	1.19	0.69	0.16	−0.14
Rough Rice	1.10	1.08	1.36	1.17	1.08	1.11
Soybean	1.30	1.01	0.84	0.06	−0.26	−0.48
Soybean Oil	5.04	5.30	5.18	4.56	3.62	2.91
Soybean Meal	−0.33	−0.87	−1.08	−1.81	−1.88	−1.97
Canola	0.62	0.88	0.81	0.36	−0.09	−0.37
Coffee	2.01	1.86	1.69	1.28	1.33	1.99
Cocoa	3.14	2.58	2.01	1.48	1.73	2.52
Sugar #11	3.81	3.96	3.93	3.45	2.38	1.29
Cotton #2	2.52	2.56	2.16	1.56	1.16	0.96
Orange Juice	2.25	2.08	1.97	1.86	1.85	1.94
Live Cattle	0.18	0.15	−0.08	−0.23	−0.06	0.13
Feeder Cattle	−0.14	−0.25	−0.57	−0.71	−0.47	−0.27
Lean Hogs	0.90	1.17	1.17	1.37	1.61	1.70
Lumber	1.65	1.33	0.69	0.38	0.48	0.40
Class III Milk	1.04	1.08	0.88	0.79	0.59	0.49

This table reports hedge ratios across investment horizons from 1 month to 36 months. Panel A presents results for commodity indices; Panel B presents results for individual commodity futures. Cumulative returns over each horizon are regressed on cumulative inflation. This analysis reveals whether commodities provide better short-term or long-term inflation protection. Declining hedge ratios with horizon length suggest that immediate price responses dominate, while increasing ratios indicate that price adjustments to inflation continue over extended periods.

At the index level in Panel A of Table 3, hedge ratios for energy-intensive benchmarks decline monotonically as the horizon lengthens. The GSCI Energy index, for example, exhibits strong short-term sensitivity that weakens substantially over 24- and 36-month horizons. A similar pattern is observed for the S&P GSCI and most CRB sub-indices. This decline suggests that the inflation responsiveness of commodity prices is largely contemporaneous, reflecting immediate price transmission rather than persistent long-run co-movement.

The disaggregated futures results reinforce this interpretation in Panel B of Table 3. Gasoline and crude oil display pronounced short-run hedge ratios that diminish materially at longer horizons. In contrast, precious metals exhibit relatively stable but modest coefficients across horizons, while certain agricultural commodities show mixed or even declining sensitivity.

These findings contribute to the literature by demonstrating that conclusions about commodity inflation hedging depend critically on investment horizons. Practically, commodities, especially energy, appear better suited for tactical, short-term inflation protection rather than long-term strategic hedging. Static multi-horizon allocations may therefore overstate sustained inflation protection, underscoring the importance of dynamic horizon-aware portfolio design.

4.4. Rolling Window Stability Analysis

Table 4 evaluates the stability of inflation hedge ratios using 60-month rolling regressions, providing evidence on time variation in hedging effectiveness. The results indicate that inflation sensitivity is not uniformly stable across commodities, reinforcing the importance of dynamic analysis. The GSCI Energy index exhibits exceptional stability, with 100% rolling windows consistently producing positive hedge ratios and relatively low dispersion, as shown in Table 4, Panel A. The S&P GSCI index similarly maintains a high proportion of positive windows, reflecting the dominant influence of energy exposure. In contrast, several CRB sub-indices exhibit substantial variability, characterized by lower percentages of positive windows and wider dispersion. GSCI Livestock shows particularly weak stability, suggesting limited reliability as a hedge across market environments.

Table 4. Rolling 60-month hedge ratio stability.

Panel A: Commodity Indices
Index	Mean	Std Dev	Min	Max	% Positive
CRB Metals	3.01	4.30	−6.30	18.60	82.41
CRB Textiles	0.67	1.79	−6.11	4.90	65.61
CRB Raw Industrials	1.94	2.46	−2.22	10.61	75.31
CRB Foodstuffs	2.37	3.06	−5.45	9.20	75.87
CRB Fats and Oils	2.90	4.39	−11.88	14.48	68.88
CRB Livestock	3.14	3.20	−4.57	11.80	80.61
CRB Spot Index	2.09	2.26	−3.40	9.59	86.47
GSCI Agricultural	3.41	4.95	−7.76	15.02	74.84
GSCI Energy	26.14	7.02	10.61	42.74	100.00
GSCI Industrial Metals	4.02	4.10	−5.83	13.18	81.82
GSCI Livestock	0.53	2.13	−5.18	7.98	54.50
GSCI Precious Metals	1.79	3.39	−8.48	10.64	72.43
S&P GSCI Index	12.68	6.68	−2.12	25.95	97.22
Panel B: Individual Commodity Futures
Commodity	Mean	Std Dev	Min	Max	% Positive
Gasoline RBOB	30.06	8.12	11.19	54.23	100.00
Crude Oil WTI	26.90	8.52	11.29	53.43	100.00
ULSD NY Harbor	23.92	8.95	0.21	48.35	100.00
Natural Gas	19.53	13.67	−3.61	47.28	97.56
Gold	1.51	2.86	−7.27	11.56	70.83
Silver	2.59	6.49	−17.34	25.67	64.69
Platinum	2.53	5.07	−12.55	12.28	71.92
Palladium	3.49	8.53	−17.86	24.23	61.55
Copper	4.01	4.56	−6.39	16.93	80.62
Corn	3.71	5.10	−7.94	17.63	75.61
Wheat	1.18	5.79	−13.39	13.13	55.01
Oats	1.16	6.47	−17.27	15.38	59.76
Rough Rice	2.54	5.24	−7.42	16.55	60.76
Soybean	1.01	4.82	−9.93	13.76	49.32
Soybean Oil	3.63	7.95	−13.03	26.55	64.50
Soybean Meal	0.70	5.30	−7.44	17.14	37.94
Canola	−0.97	5.61	−17.41	8.33	47.28
Coffee	1.39	6.67	−20.09	17.48	57.31
Cocoa	2.12	4.37	−10.63	11.52	69.38
Sugar #11	4.46	9.31	−21.19	31.70	77.78
Cotton #2	2.01	4.97	−10.96	16.99	61.65
Orange Juice	1.68	5.63	−14.65	17.16	61.67
Live Cattle	0.28	2.53	−6.51	6.18	52.03
Feeder Cattle	−0.28	2.66	−8.06	6.16	48.33
Lean Hogs	0.39	4.47	−11.35	16.23	62.46
Lumber	2.26	7.87	−10.39	32.57	56.98
Class III Milk	2.57	2.30	−2.91	7.98	88.62

This table reports descriptive statistics of hedge ratios using 60-month rolling window estimation. Panel A presents results for commodity indices; Panel B presents results for individual commodity futures. For each commodity, we report the mean, standard deviation, minimum, and maximum hedge ratios across all rolling windows, along with the percentage of windows exhibiting positive hedge ratios. High standard deviation and low percentage positive indicate unstable hedging relationships that may limit practical implementation. Stable hedging relationships are characterized by consistent positive coefficients across different market environments.

The individual futures results in Table 4, Panel B sharpen these findings. Energy contracts such as Gasoline, Crude Oil, and ULSD maintain consistently positive hedge ratios across virtually all windows, whereas precious metals and agricultural commodities exhibit considerable instability. Gold and silver, for example, show only moderate proportions of positive windows and high variability, indicating regime-dependent behavior.

Findings in Table 4 demonstrate that average hedge ratios may conceal substantial temporal instability. Practically, effective inflation hedging requires sector selection and active monitoring, as static allocations outside the energy complex may deliver inconsistent protection across economic regimes. Consistent with Spierdijk and Umar (2014), Naraidoo and Paez-Farrell (2022), and Hadad et al. (2024), the results confirm that commodity–inflation relationships evolve over time. However, this study advances the literature by identifying that energy commodities exhibit relatively stable hedge ratios, whereas metals and agricultural commodities display episodic and less predictable behavior. This distinction helps reconcile conflicting findings in prior studies and highlights stability as a critical criterion for practical hedging effectiveness.

4.5. Granger Causality Analysis

Table 5 reports Granger causality tests between CPI inflation and commodity returns, providing insight into the direction of predictive relationships. The results suggest that inflation predominantly drives commodity price movements rather than the reverse, particularly within the energy sector.

Table 5. Granger causality tests.

Panel A: Commodity Indices
Index	CPI→Comm p-Val	CPI Causes?	Comm→CPI p-Val	Comm Causes?
CRB Metals	0.66	No	0.01	Yes
CRB Textiles	0.01	Yes	0.01	Yes
CRB Raw Industrials	0.01	Yes	0.00	Yes
CRB Foodstuffs	0.00	Yes	0.06	No
CRB Fats and Oils	0.00	Yes	0.22	No
CRB Livestock	0.00	Yes	0.20	No
CRB Spot Index	0.01	Yes	0.01	Yes
GSCI Agricultural	0.84	No	0.43	No
GSCI Energy	0.00	Yes	0.36	No
GSCI Industrial Metals	0.09	No	0.92	No
GSCI Livestock	0.06	No	0.02	Yes
GSCI Precious Metals	0.24	No	0.33	No
S&P GSCI Index	0.00	Yes	0.01	Yes
Panel B: Individual Commodity Futures
Commodity	CPI→Comm p-Val	CPI Causes?	Comm→CPI p-Val	Comm Causes?
Gasoline RBOB	0.000	Yes	0.220	No
Crude Oil WTI	0.000	Yes	0.307	No
LSD NY Harbor	0.000	Yes	0.013	Yes
Natural Gas	0.202	No	0.581	No
Gold	0.107	No	0.344	No
Silver	0.052	No	0.022	Yes
Platinum	0.066	No	0.326	No
Palladium	0.392	No	0.281	No
Copper	0.527	No	0.722	No
Corn	0.751	No	0.046	Yes
Wheat	0.756	No	0.068	No
Oats	0.973	No	0.187	No
Rough Rice	0.194	No	0.691	No
Soybean	0.800	No	0.046	Yes
Soybean Oil	0.380	No	0.084	No
Soybean Meal	0.188	No	0.020	Yes
Canola	0.532	No	0.023	Yes
Coffee	0.289	No	0.285	No
Cocoa	0.827	No	0.470	No
Sugar #11	0.879	No	0.776	No
Cotton #2	0.392	No	0.006	Yes
Orange Juice	0.967	No	0.179	No
Live Cattle	0.023	Yes	0.065	No
Feeder Cattle	0.048	Yes	0.562	No
Lean Hogs	0.293	No	0.129	No
Lumber	0.132	No	0.643	No
Class III Milk	0.290	No	0.899	No

This table presents Granger causality tests examining the predictive relationships between inflation and commodity returns using 4 lags. Panel A presents results for commodity indices; Panel B presents results for individual commodity futures. We test both directions: whether CPI inflation Granger-causes commodity returns (CPI→Comm) and whether commodity returns Granger-cause inflation (Comm→CPI). p-values below 0.05 indicate statistically significant predictive power at the 5% level. Bidirectional causality suggests mutual feedback between commodity prices and inflation, while unidirectional causality identifies the dominant direction of information flow.

At the index level, several indices, including CRB Textiles, CRB Raw Industrials, CRB Spot Index, and S&P GSCI, present significant bidirectional causality, while CRB Foodstuffs, CRB Fats and Oils, CRB Livestock, and GSCI Energy exhibit unidirectional causality from CPI to commodity returns. This finding supports the interpretation that energy markets respond to inflationary pressures rather than systematically forecasting them. Reverse causality from commodity to CPI is found for CRB Metals, GSCI Livestock. GSCI Agricultural, GSCI Industrial Metals, and GSCI Precious Metals, indicating reverse causality is neither pervasive nor economically dominant. The individual futures results reinforce this pattern. Gasoline, crude oil, and ULSD show strong evidence that inflation Granger-causes returns, consistent with their contemporaneous hedging role. Precious metals display no robust predictive linkage in either direction.

These findings can clarify that commodity inflation hedging operates primarily through price transmission rather than forward-looking inflation forecasting, which implies that energy contracts function as responsive hedges rather than leading indicators of inflation dynamics. While Mahdavi and Zhou (1997) and Garratt and Petrella (2022) emphasize the predictive role of commodity prices for inflation, these findings suggest that, for most commodities, the dominant relationship runs from inflation to commodity returns. This aligns more closely with transmission-based interpretations such as Orlowski (2017) and Mello and Ponce (2025).

4.6. Out-of-Sample Validation

Table 6 assesses the stability of in-sample hedge ratios using a 70/30 split, thereby evaluating whether documented inflation-hedging relationships persist outside the estimation window. All 13 commodity indices satisfy the stability criterion, with out-of-sample hedging effectiveness remaining within 15 percentage points of in-sample estimates. GSCI Energy retains substantial explanatory power out-of-sample (declining modestly from 37% to 30%), while the S&P GSCI exhibits improved performance (16% to 24%). These results indicate that energy-driven inflation sensitivity is not sample-specific but structurally persistent.

Table 6. Out-of-sample hedging performance.

Panel A: Commodity Indices
Index	In-Sample HR	In-Sample HE	Out-of-Sample HE	Difference	Stable?
CRB Metals	1.29	0.01	0.05	0.04	Yes
CRB Textiles	1.47	0.03	0.04	0.01	Yes
CRB Raw Industrials	1.54	0.04	0.11	0.07	Yes
CRB Foodstuffs	2.66	0.07	0.10	0.04	Yes
CRB Fats and Oils	3.39	0.04	0.07	0.04	Yes
CRB Livestock	2.98	0.04	0.06	0.01	Yes
CRB Spot Index	1.97	0.07	0.15	0.07	Yes
GSCI Agricultural	3.44	0.04	0.05	0.01	Yes
GSCI Energy	21.18	0.37	0.30	−0.08	Yes
GSCI Industrial Metals	2.67	0.02	0.05	0.03	Yes
GSCI Livestock	0.55	0.00	0.01	0.01	Yes
GSCI Precious Metals	3.02	0.03	0.00	−0.03	Yes
S&P GSCI Index	6.80	0.16	0.24	0.08	Yes
Panel B: Individual Commodity Futures
Commodity	In-Sample HR	In-Sample HE	Out-of-Sample HE	Difference	Stable?
Gasoline RBOB	25.90	0.47	0.36	−0.11	Yes
Crude Oil WTI	21.00	0.32	0.30	−0.02	Yes
ULSD NY Harbor	12.53	0.20	0.28	0.08	Yes
Natural Gas	17.64	0.11	−0.05	−0.16	No
Gold	1.62	0.01	0.00	−0.01	Yes
Silver	0.93	0.00	0.02	0.01	Yes
Platinum	0.80	0.00	0.02	0.02	Yes
Palladium	1.92	0.00	0.00	0.00	Yes
Copper	−0.25	0.00	−0.01	−0.01	Yes
Corn	2.10	0.01	0.05	0.03	Yes
Wheat	1.21	0.00	0.01	0.01	Yes
Oats	0.64	0.00	0.01	0.01	Yes
Rough Rice	2.96	0.01	−0.01	−0.02	Yes
Soybean	−0.66	0.00	−0.02	−0.02	Yes
Soybean Oil	3.17	0.01	0.08	0.07	Yes
Soybean Meal	−1.89	0.00	−0.03	−0.03	Yes
Canola	0.45	0.00	0.00	0.00	Yes
Coffee	1.68	0.00	0.01	0.01	Yes
Cocoa	2.40	0.01	0.03	0.02	Yes
Sugar #11	3.08	0.01	0.03	0.03	Yes
Cotton #2	0.28	0.00	0.01	0.01	Yes
Orange Juice	1.40	0.00	0.01	0.01	Yes
Live Cattle	−0.22	0.00	0.00	0.00	Yes
Feeder Cattle	−1.17	0.01	−0.03	−0.03	Yes
Lean Hogs	−0.08	0.00	0.00	0.00	Yes
Lumber	0.39	0.00	0.00	0.00	Yes
Class III Milk	1.70	0.02	0.04	0.03	Yes

This table presents out-of-sample validation using a 70/30 data split. Panel A presents results for commodity indices; Panel B presents results for individual commodity futures. Hedge ratios are estimated on the first 70% of observations (in-sample) and tested on the remaining 30% (out-of-sample). We report hedging effectiveness (R-squared) for both periods and their difference. ‘Stable = Yes’ indicates that the absolute difference between in-sample and out-of-sample hedging effectiveness is less than 15 percentage points, suggesting robust and reliable hedging relationships.

Among individual futures, 26 of 27 contracts meet the stability threshold. Gasoline, crude oil, and ULSD maintain strong and economically meaningful hedging effectiveness across subsamples. Natural gas is the sole exception, with out-of-sample effectiveness turning negative, reflecting greater structural instability. Precious metals and most agricultural commodities display low but stable performance, consistent with earlier findings.

These results reinforce our contribution that energy-based inflation hedging is robust, while non-energy commodities exhibit weaker yet generally stable relationships, supporting targeted rather than broad commodity allocations. While prior studies, including Hadad et al. (2024) and Nakagawa and Sakemoto (2023), emphasize conditional or time-varying performance, they often do not directly assess out-of-sample persistence. These results show that energy-based hedging relationships remain robust beyond the estimation window, whereas certain commodities, such as natural gas, exhibit instability. This distinction reinforces the importance of robustness checks in evaluating practical hedging strategies.

4.7. Regime-Dependent Analysis

Table 7 reports hedge ratios estimated across four inflation regimes of disinflation, moderate, high, and very high inflation, and directly examines regime dependence, a major contribution of this study. Most CRB sub-indices exhibit declining hedge ratios as inflation intensifies. For example, CRB Fats and Oils and CRB Livestock display strong coefficients during moderate inflation but materially weaker sensitivity during very high inflation. This pattern suggests that certain commodity sectors co-move with inflation under stable price environments but do not scale proportionally during inflationary extremes. On the contrary, GSCI Energy maintains large and economically meaningful hedge ratios in both high and very high inflation regimes, indicating persistent responsiveness when protection is most valuable. The S&P GSCI similarly retains positive sensitivity, reflecting its energy concentration.

Table 7. Hedge ratios by inflation regime.

Panel A: Commodity Indices
Index	Moderate (0–3%)	High (3–6%)	Very High (>6%)
CRB Metals	6.39	7.27	2.79
CRB Textiles	0.68	2.61	1.58
CRB Raw Industrials	5.35	4.78	2.20
CRB Foodstuffs	6.60	4.80	2.79
CRB Fats and Oils	13.08	6.23	3.81
CRB Livestock	11.81	6.15	2.81
CRB Spot Index	5.54	4.77	2.44
GSCI Agricultural	-	5.76	4.42
GSCI Energy	-	26.43	20.51
GSCI Industrial Metals	-	8.13	2.53
GSCI Livestock	-	2.62	0.37
GSCI Precious Metals	-	4.35	0.70
S&P GSCI Index	-	16.92	10.54
Panel B: Individual Commodity Futures
Commodity	Moderate (0–3%)	High (3–6%)	Very High (>6%)
Gasoline RBOB	33.49	23.74	-
Crude Oil WTI	29.74	17.33	-
ULSD NY Harbor	24.40	19.17	4.72
Natural Gas	9.56	22.29	-
Gold	3.92	−0.37	3.91
Silver	7.77	1.40	4.84
Platinum	6.95	5.25	3.39
Palladium	6.71	4.25	2.17
Copper	9.20	2.91	2.11
Corn	5.76	5.52	5.10
Wheat	2.90	2.41	7.08
Oats	4.70	2.35	3.34
Rough Rice	3.33	−1.50	-
Soybean	3.71	6.85	0.72
Soybean Oil	7.01	8.61	7.39
Soybean Meal	1.62	6.11	−2.83
Canola	1.44	4.17	2.50
Coffee	3.59	4.98	−0.47
Cocoa	7.14	4.77	1.27
Sugar #11	5.06	1.54	11.82
Cotton #2	7.67	3.14	0.87
Orange Juice	1.20	5.78	−0.77
Live Cattle	1.38	0.93	−1.58
Feeder Cattle	1.85	0.56	−2.70
Lean Hogs	2.72	1.84	−2.85
Lumber	7.67	2.44	2.74
Class III Milk	4.33	0.50	-

This table reports hedge ratios across different inflation environments. Panel A presents results for commodity indices; Panel B presents results for individual commodity futures. Inflation regimes are defined based on trailing 12-month CPI inflation: Moderate (0–3%), High (3–6%), and Very High (>6%). Separate hedge ratios are estimated within each regime. This analysis addresses whether commodities provide enhanced protection during high inflation episodes when hedging is most valuable. A dash (-) indicates insufficient observations (fewer than 30) within that regime for reliable estimation.

The individual commodity results in Table 7, Panel B confirm these distinctions. Gasoline and crude oil remain strongly inflation-sensitive in moderate and high regimes. At the same time, gold offers limited protection against moderate inflation but exhibits improved sensitivity under very high inflation, consistent with its conditional safe-haven behavior. Several livestock contracts turn negative during very high inflation, highlighting regime fragility. Conclusively, these findings demonstrate that inflation hedging is regime-contingent rather than uniform, supporting our contribution that dynamic, sector-aware allocation is essential for effective inflation risk management.

Consistent with Brière and Signori (2012), Valadkhani et al. (2022), Valadkhani and O’Mahony (2024), and Liu et al. (2023), the results confirm that inflation hedging varies across macroeconomic states. However, this study further shows that energy commodities maintain economically meaningful sensitivity even in high-inflation regimes, while gold’s hedging properties become more pronounced primarily under extreme inflation. In contrast, several non-energy commodities exhibit weakened or reversed relationships, highlighting that broad commodity exposure may be insufficient when inflation risk intensifies.

4.8. Markov-Switching VECM Analysis

Table 8 reports regime-dependent error correction coefficients from the MS-VECM framework, allowing us to distinguish between contemporaneous inflation sensitivity and long-run equilibrium adjustment mechanisms across stable and turbulent states. At the index level, all 13 commodity indices except GSCI Livestock, GSCI Precious Metals, and S&P GSCI display predominantly negative error correction coefficients in both regimes, with magnitudes generally larger in the turbulent regime. For example, GSCI Energy, despite exhibiting the strongest static hedge ratios earlier, shows a significantly negative adjustment coefficient in the high-volatility state. Similar patterns are observed for the S&P GSCI and most CRB sub-indices. A negative and significant coefficient implies that commodity prices adjust away from, rather than toward, a long-run inflation equilibrium following shocks. No index satisfies the criterion of positive and statistically significant error correction consistent with structural long-run hedging. Even GSCI Precious Metals, which exhibits a small positive coefficient in the stable regime, lacks statistical significance.

Table 8. MS-VECM results.

Panel A: Commodity Indices
Index	EC(R1)	t-Stat	EC(R2)	t-Stat	Hedges?
CRB Metals	−0.01	−1.28	−0.03	−3.35	No
CRB Textiles	−0.01	−1.86	−0.05	−4.35	No
CRB Raw Industrials	−0.01	−0.95	−0.03	−4.05	No
CRB Foodstuffs	−0.02	−2.69	−0.03	−2.90	No
CRB Fats and Oils	−0.03	−4.28	−0.05	−4.13	No
CRB Livestock	−0.03	−3.76	−0.06	−4.61	No
CRB Spot Index	−0.02	−3.10	−0.02	−2.80	No
GSCI Agricultural	−0.01	−0.75	−0.04	−2.66	No
GSCI Energy	−0.01	−0.72	−0.09	−4.35	No
GSCI Ind. Metals	−0.02	−1.94	−0.06	−2.99	No
GSCI Livestock	0.00	0.03	−0.12	−4.60	No
GSCI Prec. Metals	0.01	1.19	−0.03	−2.38	No
S&P GSCI	0.00	−0.63	−0.04	−3.11	No
Panel B: Individual Commodity Futures
Commodity	EC(R1)	t-Stat	EC(R2)	t-Stat	Hedges?
Gasoline RBOB	−0.01	−0.90	−0.05	−2.93	No
Crude Oil WTI	0.00	0.01	−0.02	−1.35	No
ULSD NY Harbor	−0.01	−0.53	−0.04	−2.98	No
Natural Gas	−0.01	−1.27	−0.03	−2.04	No
Gold	0.01	1.55	−0.02	−2.31	No
Silver	0.01	0.81	−0.02	−1.98	No
Platinum	0.00	−0.49	−0.02	−1.59	No
Palladium	0.00	0.07	−0.04	−2.67	No
Copper	0.00	−0.02	−0.03	−2.90	No
Corn	0.00	−0.46	−0.02	−2.78	No
Wheat	0.00	0.05	−0.01	−1.93	No
Oats	0.00	−0.07	−0.03	−2.97	No
Rough Rice	−0.03	−2.04	−0.02	−1.56	No
Soybean	0.00	−0.75	−0.01	−0.84	No
Soybean Oil	0.00	−1.13	−0.02	−2.75	No
Soybean Meal	0.00	−1.07	0.00	0.20	No
Canola	−0.02	−1.45	−0.02	−1.56	No
Coffee	0.00	0.41	−0.04	−3.75	No
Cocoa	−0.01	−1.36	−0.01	−1.15	No
Sugar #11	−0.02	−2.02	−0.02	−2.21	No
Cotton #2	−0.01	−1.64	−0.01	−1.30	No
Orange Juice	0.00	−0.63	−0.03	−3.01	No
Live Cattle	−0.01	−0.53	−0.03	−2.43	No
Feeder Cattle	0.00	0.23	−0.05	−3.45	No
Lean Hogs	−0.01	−1.87	−0.01	−1.16	No
Lumber	−0.01	−2.39	−0.02	−1.74	No
Class III Milk	−0.02	−1.58	−0.07	−3.03	No

This table presents Markov-Switching Vector Error Correction Model (MS-VECM) results. Panel A presents results for commodity indices; Panel B presents results for individual commodity futures. Two volatility-based regimes are identified using 24-month rolling volatility: Regime 1 (stable) and Regime 2 (turbulent). The error correction coefficients EC(R1) and EC(R2) measure the adjustment speed toward long-run equilibrium in each regime. Positive and significant coefficients indicate that commodity prices adjust to restore the cointegrating relationship with inflation, providing a dynamic hedging mechanism. ‘Hedges = Yes’ requires EC > 0 with |t| > 1.96 in at least one regime.

The individual commodity results reinforce this interpretation. Energy contracts such as gasoline and crude oil, which were previously identified as strong contemporaneous hedges, do not demonstrate positive and significant long-run error correction in either regime. Precious metals and agricultural commodities similarly fail to exhibit equilibrium adjustment consistent with persistent inflation hedging. Notably, several contracts, including Gasoline, ULSD, Coffee, and Feeder Cattle, exhibit stronger negative adjustments in turbulent regimes, indicating heightened divergence during macroeconomic stress.

The MS-VECM results provide a notable contrast to Liu et al. (2023), which document regime-dependent long-run hedging relationships, particularly for metals. Our findings do not support stable cointegrating behavior between commodity returns and inflation across regimes. Instead, even commodities with strong contemporaneous hedging properties, such as crude oil and gasoline, fail to exhibit consistent long-run error-correction dynamics. This suggests that commodity-based inflation hedging is better characterized as a short-run, state-dependent adjustment mechanism rather than a persistent long-run equilibrium relationship. The divergence from Liu et al. (2023) highlights the importance of sample scope, asset coverage, and model specification in interpreting regime-based hedging results.

4.9. Robustness Analysis

We conduct robustness checks to ensure that our main findings are not sensitive to specific methodological choices. The results, reported in Table 9, Table 10 and Table 11, provide strong supporting evidence for the paper’s central conclusions across alternative rolling window specifications, MS-VECM volatility windows, and distinct historical subperiods.

Table 9. Robustness of rolling window analysis to alternative window lengths.

Panel A: Individual Commodity Futures
Commodity	36-Mo Mean	% Pos	48-Mo Mean	% Pos	60-Mo Mean	% Pos	72-Mo Mean	% Pos
Gasoline RBOB	29.99	100.0	30.00	100.0	30.10	100.0	30.09	100.0
Crude Oil WTI	26.50	100.0	27.04	100.0	27.06	100.0	26.86	100.0
ULSD NY Harbor	23.30	99.3	23.46	100.0	23.51	100.0	23.44	100.0
Natural Gas	18.50	92.2	19.09	95.1	19.08	97.6	19.00	99.7
Gold	1.34	68.4	1.43	69.3	1.59	71.4	1.70	73.5
Silver	2.63	64.1	2.51	61.2	2.67	65.2	2.65	67.5
Platinum	2.58	73.2	2.45	73.1	2.51	72.4	2.68	73.7
Palladium	4.10	64.6	3.74	62.8	3.50	62.3	3.39	60.0
Copper	3.50	73.1	3.82	75.3	4.01	80.6	4.05	84.6
Corn	3.42	67.3	3.56	73.7	3.71	75.6	3.77	74.7
Wheat	1.04	49.2	1.10	52.3	1.18	55.0	1.28	57.2
Oats	0.86	61.3	0.92	59.9	1.16	59.8	1.27	59.4
Rough Rice	1.99	49.9	2.19	52.1	2.11	57.3	2.05	58.7
Soybean	0.75	47.6	0.88	48.4	1.01	49.3	1.15	50.7
Soybean Oil	2.77	67.8	3.23	65.1	3.63	64.5	3.97	65.4
Soybean Meal	0.62	42.8	0.66	41.2	0.70	37.9	0.76	39.1
Canola	−1.29	42.5	−1.06	44.9	−0.90	47.6	−0.77	48.6
Coffee	1.89	58.8	1.48	54.7	1.26	56.2	1.22	56.9
Cocoa	2.22	62.7	1.92	66.5	2.12	69.4	2.28	73.6
Sugar #11	4.35	75.4	4.26	76.7	4.42	77.4	4.46	77.0
Cotton #2	1.97	60.6	1.94	60.9	2.01	61.7	2.09	61.3
Orange Juice	1.16	54.7	1.12	58.7	1.49	60.6	1.93	64.6
Lumber	2.27	52.2	2.42	55.0	2.42	58.1	2.40	61.8
Live Cattle	0.19	52.4	0.34	53.2	0.34	52.0	0.38	53.8
Feeder Cattle	−0.76	43.0	−0.47	47.4	−0.33	48.4	−0.21	50.1
Lean Hogs	0.63	59.7	0.66	62.3	0.52	63.1	0.48	64.4
Class III Milk	2.26	77.6	2.48	88.0	2.58	89.1	2.61	92.3
Panel B: Commodity Indices
Index	36-Mo Mean	% Pos	48-Mo Mean	% Pos	60-Mo Mean	% Pos	72-Mo Mean	% Pos
CRB Metals	2.78	75.5	2.95	78.2	3.01	82.4	3.04	87.0
CRB Textiles	0.57	59.5	0.60	59.6	0.67	65.6	0.71	66.1
CRB Raw Industrials	1.78	73.3	1.87	73.6	1.94	75.3	1.98	81.8
CRB Foodstuffs	2.15	69.3	2.28	72.5	2.37	75.9	2.45	78.6
CRB Fats and Oils	2.46	71.5	2.74	70.2	2.90	68.9	3.05	73.7
CRB Livestock	2.87	75.0	3.05	79.0	3.14	80.6	3.23	82.2
CRB Spot Index	1.90	77.3	2.01	80.1	2.09	86.5	2.15	92.7
GSCI Agricultural	3.35	69.6	3.46	72.0	3.54	75.2	3.53	76.7
GSCI Energy	25.92	100.0	26.21	100.0	26.25	100.0	26.10	100.0
GSCI Ind. Metals	3.77	78.1	3.89	79.7	4.02	82.2	4.06	84.5
GSCI Livestock	0.27	49.0	0.51	54.0	0.55	55.2	0.62	56.0
GSCI Prec. Metals	1.65	68.8	1.71	69.7	1.88	72.6	1.99	75.0
S&P GSCI	12.32	92.8	12.52	95.4	12.60	97.3	12.55	99.7

This table reports the robustness of rolling window hedge ratio estimates to alternative window lengths (36, 48, 60, and 72 months). Panel A presents results for commodity indices; Panel B presents results for individual commodity futures. Mean is the average hedge ratio across all rolling windows. % Pos is the percentage of rolling windows with positive hedge ratios. The baseline 60-month window from the main analysis is included for comparison.

Table 10. Hedge ratios across subperiods.

Panel A: Individual Commodity Futures
Commodity	1959–1989 HR	N	1990–2019 HR	N	2020–2025 HR	N	COVID HR	N
Gasoline RBOB	30.61 ***	61	26.50 ***	360	25.76 ***	71	27.88 ***	36
Crude Oil WTI	29.11 ***	82	20.97 ***	360	26.51 **	71	29.60 ***	36
ULSD NY Harbor	6.73 *	134	21.30 ***	360	19.12 ***	71	19.97 ***	36
Natural Gas	-	-	16.95 ***	357	4.94	71	6.78	36
Gold	1.43	180	3.20 ***	360	−1.34	71	−0.64	36
Silver	2.11	319	5.27 ***	360	2.34	71	3.37	36
Platinum	1.61	262	6.74 ***	360	1.69	71	1.31	36
Palladium	−1.85	156	6.79 **	360	−0.57	71	−1.80	36
Copper	−1.10	366	8.83 ***	360	2.06	71	3.08	36
Corn	2.51	366	5.16 **	360	7.20 ***	71	5.65 **	36
Wheat	0.89	366	3.55	360	5.47	71	5.19	36
Oats	1.80	366	3.26	360	5.27 *	71	3.24	36
Rough Rice	−3.56	41	2.98	360	-	-	-	-
Soybean	−0.29	366	4.14 *	360	2.62	71	1.73	36
Soybean Oil	4.33 *	366	5.76 **	360	7.39 ***	71	6.86 **	36
Soybean Meal	−2.01	366	3.37	360	−1.56	71	−3.05	36
Canola	0.48	180	0.65	360	4.79 **	71	4.18 **	36
Coffee	0.18	209	3.80 **	360	1.84	71	4.30	36
Cocoa	2.80 *	366	4.58 **	360	3.40	71	2.10	36
Sugar #11	4.40	348	4.47 **	360	6.30	71	5.74	36
Cotton #2	−0.32	366	5.42 ***	360	8.32 ***	71	6.99 **	36
Orange Juice	1.28	275	3.31	360	0.88	71	−2.55	36
Lumber	−0.88	243	2.27	360	19.37 ***	65	18.95 ***	30
Live Cattle	−0.89	301	1.01	348	-	-	-	-
Feeder Cattle	−1.56	217	1.33	360	0.94	51	0.98	36
Lean Hogs	−0.67	286	1.00	360	2.64	71	1.67	36
Class III Milk	-	-	1.74 **	234	5.26 ***	71	5.41 **	36
Panel B: Commodity Indices
Index	1947–1989 HR	N	1990–2019 HR	N	2020–2025 HR	N
CRB Metals	1.10 *	515	8.37 **	360	2.63	71
CRB Textiles	1.55 ***	515	1.13 *	360	1.86 **	71
CRB Raw Industrials	1.43 ***	515	4.80 ***	360	2.09	71
CRB Foodstuffs	2.90 ***	515	3.43 **	360	5.06 ***	71
CRB Fats and Oils	3.50 ***	515	6.09 **	360	5.79 ***	71
CRB Livestock	2.95 ***	515	5.05 **	360	3.07	71
CRB Spot Index	2.00 ***	515	4.23 ***	360	3.30 ***	71
GSCI Agricultural	3.73 **	240	4.79 ***	360	5.55 ***	71
GSCI Energy	27.05 ***	84	21.47 ***	360	20.88 ***	71
GSCI Ind. Metals	0.40	156	6.50 ***	360	2.72	71
GSCI Livestock	0.21	239	0.87	360	3.65	71
GSCI Prec. Metals	3.24	201	3.60 ***	360	−1.27	71

This table reports hedge ratios across different subperiods. Panel A presents results for individual commodity futures (1959–1989, 1990–2019, 2020–2025, and COVID); Panel B presents results for commodity indices (1947–1989, 1990–2019, 2020–2025). HR is the optimal hedge ratio estimated using OLS with Newey-West standard errors. N is the number of observations. COVID refers to the COVID-19 pandemic period (January 2020 to December 2022). Statistical significance is denoted by *** (p < 0.01), ** (p < 0.05), and * (p < 0.10). A dash (-) indicates insufficient observations (fewer than 30) for reliable estimation.

Table 11. Robustness of MS-VECM analysis to alternative volatility windows.

Panel A: Individual Commodity Futures
Commodity	24-Mo EC(R2)	t-Stat	36-Mo EC(R2)	t-Stat	48-Mo EC(R2)	t-Stat	60-Mo EC(R2)	t-Stat
Gasoline RBOB	−0.0510	−3.03	−0.0682	−4.70	−0.0656	−4.26	−0.0535	−3.60
Crude Oil WTI	−0.0115	−1.03	−0.0279	−2.54	−0.0262	−2.41	−0.0201	−1.90
ULSD NY Harbor	−0.0300	−2.46	−0.0356	−2.90	−0.0502	−3.67	−0.0309	−2.28
Natural Gas	−0.0175	−1.39	−0.0182	−1.40	−0.0136	−1.02	−0.0102	−0.79
Gold	−0.0138	−1.64	−0.0214	−2.10	−0.0276	−2.53	−0.0290	−2.70
Silver	−0.0341	−3.27	−0.0349	−3.20	−0.0494	−3.58	−0.0524	−3.54
Platinum	−0.0188	−1.56	−0.0180	−1.56	−0.0127	−1.10	−0.0095	−0.88
Palladium	−0.0400	−2.51	−0.0482	−3.24	−0.0715	−4.35	−0.0667	−3.53
Copper	−0.0169	−2.09	−0.0202	−2.43	−0.0181	−2.26	−0.0082	−1.04
Corn	−0.0233	−2.72	−0.0227	−2.62	−0.0215	−2.54	−0.0228	−2.46
Wheat	−0.0135	−2.27	−0.0137	−2.31	−0.0127	−2.10	−0.0119	−1.92
Oats	−0.0235	−2.62	−0.0262	−2.85	−0.0291	−3.32	−0.0261	−2.96
Rough Rice	−0.0149	−1.09	−0.0130	−0.91	−0.0211	−1.48	−0.0274	−1.73
Soybean	−0.0023	−0.29	−0.0076	−0.86	−0.0084	−0.96	−0.0118	−1.28
Soybean Oil	−0.0154	−2.26	−0.0157	−2.16	−0.0187	−2.43	−0.0204	−2.58
Soybean Meal	0.0028	0.47	−0.0050	−0.87	−0.0049	−0.76	−0.0036	−0.55
Canola	−0.0142	−1.49	−0.0142	−1.59	−0.0195	−2.30	−0.0217	−2.56
Coffee	−0.0299	−3.20	−0.0287	−2.62	−0.0282	−2.09	−0.0207	−1.55
Cocoa	−0.0027	−0.52	−0.0070	−1.36	−0.0055	−1.02	−0.0067	−1.24
Sugar #11	−0.0145	−1.99	−0.0179	−2.53	−0.0146	−2.02	−0.0152	−2.08
Cotton #2	−0.0115	−1.50	−0.0084	−1.14	−0.0088	−1.19	−0.0142	−1.86
Orange Juice	−0.0186	−2.21	−0.0308	−3.17	−0.0334	−2.88	−0.0305	−2.78
Lumber	−0.0157	−1.79	−0.0157	−1.87	−0.0182	−2.24	−0.0130	−1.64
Live Cattle	−0.0351	−2.93	−0.0373	−3.12	−0.0384	−3.11	−0.0331	−2.75
Feeder Cattle	−0.0377	−2.87	−0.0295	−2.31	−0.0166	−1.44	−0.0166	−1.60
Lean Hogs	−0.0023	−0.26	−0.0052	−0.61	−0.0088	−1.05	−0.0131	−1.59
Class III Milk	−0.0526	−2.56	−0.0361	−1.77	−0.0406	−2.10	−0.0334	−1.64
Panel B: Commodity Indices
Index	24-Mo EC(R2)	t-Stat	36-Mo EC(R2)	t-Stat	48-Mo EC(R2)	t-Stat	60-Mo EC(R2)	t-Stat
CRB Metals	−0.0320	−3.53	−0.0338	−3.50	−0.0284	−2.87	−0.0215	−2.25
CRB Textiles	−0.0449	−4.00	−0.0471	−4.18	−0.0698	−6.05	−0.0546	−4.37
CRB Raw Industrials	−0.0326	−4.09	−0.0370	−4.55	−0.0410	−4.96	−0.0399	−3.82
CRB Foodstuffs	−0.0282	−3.30	−0.0295	−3.36	−0.0292	−3.53	−0.0336	−3.70
CRB Fats and Oils	−0.0421	−3.64	−0.0439	−4.17	−0.0481	−4.39	−0.0413	−3.63
CRB Livestock	−0.0577	−4.76	−0.0551	−4.41	−0.0579	−4.85	−0.0512	−4.13
CRB Spot Index	−0.0222	−3.14	−0.0215	−3.04	−0.0221	−3.32	−0.0329	−4.27
GSCI Agricultural	−0.0358	−2.73	−0.0363	−2.49	−0.0585	−3.46	−0.0663	−3.87
GSCI Energy	−0.0659	−3.24	−0.0676	−3.78	−0.0604	−3.66	−0.0494	−2.95
GSCI Ind. Metals	−0.0496	−2.75	−0.0519	−2.90	−0.0394	−2.24	−0.0394	−2.32
GSCI Livestock	−0.1176	−4.48	−0.1422	−4.73	−0.1453	−4.62	−0.1212	−4.22
GSCI Prec. Metals	−0.0308	−2.59	−0.0328	−2.37	−0.0321	−2.29	−0.0337	−2.30
S&P GSCI	−0.0338	−3.12	−0.0344	−3.39	−0.0414	−3.55	−0.0373	−3.22

This table reports the robustness of MS-VECM error correction coefficients to alternative volatility window lengths (24, 36, 48, and 60 months) used for regime identification. Panel A presents results for individual commodity futures; Panel B presents results for commodity indices. EC(R2) is the error correction coefficient in Regime 2 (turbulent/high volatility). The baseline 24-month window from the main analysis is included for comparison.

Table 9 examines rolling window robustness across 36-, 48-, 60-, and 72-month windows. Energy commodities maintain 100% positive hedge ratios across all specifications, while gold shows only 68–74% positive regardless of window length. This confirms that energy’s hedging dominance and gold’s instability are not artifacts of the baseline 60-month window choice.

Table 10 presents subsample analysis across three periods (1959–1989, 1990–2019, 2020–2025) plus the COVID episode (2020–2022). Energy commodities show strong and significant hedging across all subperiods, with hedge ratios highest during high-inflation periods. Critically, gold’s hedge ratio turns negative during 2020–2025 (−1.34) and the COVID period (−0.64), directly contradicting the belief that gold provides protection when inflation is elevated. This finding suggests gold may be a safe haven during market stress but not a systematic inflation hedge.

Table 11 examines MS-VECM robustness across 24-, 36-, 48-, and 60-month volatility windows. Negative error correction coefficients persist across all specifications for all commodities, confirming that the MS-VECM puzzle is robust to methodological choices in regime identification.

The robustness analyses provide support for the paper’s main conclusions. Energy commodities demonstrate reliable inflation hedging across all specifications and historical periods, with the strongest hedging during high-inflation episodes. Precious metals—particularly gold—provide weak hedging that reverses during high-inflation periods, contradicting conventional wisdom. The MS-VECM finding of negative error correction coefficients persists across all volatility windows, confirming that hedging operates through contemporaneous price transmission rather than equilibrium adjustment. Livestock commodities consistently fail to provide inflation protection.

5. Discussion

Our empirical results reveal consistent patterns, and we would like to provide some economic interpretation. This section examines the mechanisms underlying our key findings.

5.1. Why Energy Commodities Dominate

Energy commodities demonstrate the strongest and most robust inflation-hedging properties across all methodologies. Three mechanisms explain this dominance. First, energy prices have a direct mechanical link to CPI through their weight in the consumer price index—energy represents approximately 7–8% of U.S. CPI. When oil and gasoline prices rise, CPI mechanically increases, creating contemporaneous correlation by construction.

Second, energy serves as a fundamental input to production and transportation, creating cost-push inflation channels. When energy prices rise, production and transportation costs increase across the economy, which in turn affects broader consumer prices. This transmission mechanism explains why energy hedge ratios substantially exceed CPI weight alone.

Third, energy prices respond to the same macroeconomic conditions that drive inflation—strong economic growth, monetary expansion, and supply constraints. During inflationary episodes, these factors simultaneously push up both energy prices and general price levels, reinforcing the hedging relationship.

5.2. Why Precious Metals Fail as Inflation Hedges

Our finding that gold provides weak and statistically insignificant inflation hedging contradicts widespread investor belief. Several factors explain this result. First, gold functions primarily as a safe haven during market stress and geopolitical uncertainty, not as a systematic inflation hedge. D. G. Baur and Lucey (2010) document this distinction clearly. Gold prices respond to fear and uncertainty, which may or may not coincide with inflation.

Second, gold has no direct link to CPI—it is not a consumption good and has limited industrial use. Unlike energy, there is no mechanical transmission from gold prices to consumer prices. Third, our subsample analysis reveals that gold’s hedge ratio actually turns negative during the 2020–2025 high-inflation period, precisely when hedging would be most valuable. This pattern suggests that whatever inflation-hedging properties gold exhibited historically may have weakened or reversed in the current environment.

5.3. The MS-VECM Puzzle

Our MS-VECM analysis reveals an important puzzle: despite strong positive hedge ratios from static OLS (gasoline = 25.72, crude oil = 21.93), the error correction coefficients are predominantly negative across all commodities and regimes. This finding has implications for understanding how commodity hedging operates.

Negative error correction coefficients indicate that commodity prices do not adjust toward long-run equilibrium with inflation when displaced. Instead, hedging appears to operate through direct contemporaneous price transmission rather than through dynamic equilibrium adjustment over time. Energy prices feed into CPI within the same period. This mechanism is consistent with the multi-horizon results, which show that hedge ratios decline with the investment horizon: the contemporaneous relationship is strong but does not persist through error correction.

5.4. Asymmetric Effects and Copper’s Mechanism

The asymmetric analysis reveals that many commodities respond more strongly to disinflation than inflation. Copper shows particularly pronounced asymmetry (β⁺ = −0.35 versus β⁻ = 17.05), providing no hedge against inflation increases but responding strongly to disinflation.

This pattern reflects copper’s role as a leading indicator of economic activity. Rising copper prices signal strong industrial demand and economic expansion, which typically precedes inflationary pressures. However, when economic activity weakens (associated with disinflation), copper prices fall sharply, creating an asymmetric response pattern. Our Granger causality results confirm this interpretation: copper returns Granger-cause CPI, not vice versa.

6. Conclusions

This study re-examines the inflation-hedging properties of commodity indices and commodity futures for U.S. investors, utilizing one of the broadest historical datasets in the literature. Analyzing 27 commodity futures from 1959 to 2025 and 13 commodity indices from 1947 to 2025 through multiple complementary econometric frameworks, this study documents substantial heterogeneity in hedging effectiveness across commodity sectors, investment horizons, and macroeconomic regimes. The findings further show that commodity–inflation relationships are highly dynamic and regime-dependent.

Several important conclusions emerge from the analysis. First, energy commodities consistently exhibit the strongest and most stable inflation-hedging properties across nearly all empirical specifications. Gasoline and crude oil display economically significant hedge ratios, stable rolling-window relationships, and robust out-of-sample performance. These findings are economically intuitive, given the central role of energy prices in transportation, manufacturing, utilities, and broader production costs, which are influenced by both cost- and demand-driven transmission mechanisms. The results, therefore, support the broader literature emphasizing the role of commodities in preserving purchasing power during inflationary periods (Gorton & Rouwenhorst, 2006; Erb & Harvey, 2006).

Second, industrial metals, particularly copper, provide meaningful and relatively stable inflation protection. Copper exhibits persistent hedging effectiveness across static and dynamic specifications, significant causal relationships with inflation, and stable adjustment dynamics across multiple market regimes. Its inflation sensitivity likely reflects its extensive use in industrial production, infrastructure, and electrification, allowing copper prices to rapidly incorporate expectations regarding macroeconomic activity and inflation.

Third, the findings challenge the conventional view that precious metals universally serve as reliable inflation hedges. Although gold and silver are widely regarded as inflation-protection assets, their contemporaneous hedging effectiveness appears comparatively weak and unstable. Nevertheless, regime-dependent analysis suggests that precious metals may retain value during periods of elevated macroeconomic uncertainty or severe inflationary stress, consistent with the safe-haven interpretation advanced by D. G. Baur and Lucey (2010) and the regime-switching evidence reported by Liu et al. (2023). These results imply that precious metals function more effectively as crisis-hedging assets than as consistently reliable inflation hedges.

Fourth, agricultural commodities and livestock generally exhibit weak or inconsistent inflation-hedging properties. Their price behavior appears to be driven primarily by weather conditions, biological production cycles, storage constraints, and supply-specific shocks that are only indirectly related to aggregate inflationary pressures. Consequently, broad commodity exposure alone may not provide effective inflation protection when allocations are concentrated in sectors with limited inflation sensitivity.

Finally, the analysis demonstrates that inflation-hedging relationships are strongly time-varying and regime-dependent. The MS-VECM framework identifies materially different adjustment dynamics across stable and turbulent inflationary environments, indicating that static hedge ratios may substantially misrepresent true hedging performance during periods of elevated inflation volatility. More importantly, the findings suggest that commodity inflation hedging operates primarily through contemporaneous price transmission mechanisms rather than long-run equilibrium correction, helping reconcile conflicting conclusions in the existing literature.

6.1. Implications for Investors and Policymakers

The findings carry several implications for investors, institutional portfolio managers, and policymakers. First, inflation-hedging strategies should emphasize sector-specific allocations rather than broad passive commodity exposure. Energy commodities and industrial metals provide substantially more reliable inflation protection than precious metals or agricultural commodities. This distinction is especially important for pension funds, endowments, insurance companies, and multi-asset portfolio managers seeking to preserve real purchasing power during inflationary periods.

Second, the results support the strategic and tactical role of commodity futures in diversified portfolios, as discussed by Erb and Harvey (2006) and Gorton and Rouwenhorst (2006), while also demonstrating that the effectiveness of such strategies depends critically on dynamic allocation and regime monitoring. Commodity inflation sensitivities vary materially across macroeconomic environments, implying that static buy-and-hold commodity allocations may inadequately capture inflation-protection benefits. Dynamic strategies adjusting commodity exposure in response to changing inflation regimes, monetary policy conditions, and volatility environments may therefore provide superior risk-adjusted hedging performance.

Third, the findings have important implications for monetary authorities and policymakers. The exceptionally strong inflation sensitivity of energy commodities suggests that commodity markets, particularly energy markets, play a critical role in transmitting inflationary pressures throughout the economy. This observation aligns with the growing literature examining the monetary policy–commodity nexus (Bohl et al., 2026). Because energy price shocks rapidly propagate through transportation, production, and consumer prices, commodity market dynamics may contain valuable forward-looking information regarding inflation persistence and broader macroeconomic risks.

6.2. Limitations and Future Research

Several limitations warrant acknowledgment. The analysis relies primarily on monthly data and therefore may not fully capture higher-frequency transmission dynamics. In addition, transaction costs, liquidity constraints, collateral requirements, and implementation frictions associated with commodity futures strategies are not explicitly modeled. The regime identification within the MS-VECM framework also relies on simplified volatility-based classifications rather than full maximum-likelihood regime estimation.

Future research may extend the analysis by examining alternative inflation measures, international commodity markets, and exchange-rate effects. Additional research may also investigate interactions between commodities and other inflation-sensitive asset classes, including TIPS, infrastructure, and real estate, to better inform multi-asset inflation-hedging strategies. Finally, more advanced nonlinear and state-dependent econometric frameworks may further improve understanding of commodity-inflation dynamics across changing macroeconomic environments.

Despite these limitations, this study provides robust evidence that inflation-hedging effectiveness varies substantially across commodity sectors, macroeconomic regimes, and empirical methodologies. Energy commodities and copper emerge as the most reliable inflation hedges, while precious metals and agricultural commodities provide comparatively limited and unstable protection. These findings contribute to the growing literature on commodity-based inflation hedging and provide practical guidance for investors, portfolio managers, and policymakers seeking to manage inflation risk in increasingly uncertain macroeconomic environments.