Theory and plausibility suggest that precious metal prices benefit from inflation and negative real interest rates. This makes gold, silver, platinum, and palladium natural candidates for hedges against inflationary monetary policy. Long-term empirical evidence supports the inflation-precious metal link. However, there are important qualifications. First, the equilibrium relation between consumer and metal prices can take many years to re-assert itself and short-term excesses in relative prices are common. Second, the relationship between precious metal and consumer prices can change over time as a consequence of evolving market structures or diverging supply and demand conditions. And third, the equilibrium relationship works better for gold, platinum and palladium than for silver.

The below is a summary of recent literature by Robert Brown (Economist and portfolio manager at Adrian Lee & Partners). The underlying papers are listed at the end of the post.

The post ties up with this site’s summary on macro trends.

### Cointegration and equilibrium

A __cointegrating relationship between (non-stationary) variables is said to exist when there is some linear combination of those variables which is itself stationary__. As a result, the cointegrated variables should return towards their long-run relationship over time – and hence cointegration between variables is often used to indicate an equilibrium relationship. This traditional definition of cointegration has been extended in recent econometric literature to allow the equilibrium relationship to evolve over time and for adjustment to equilibrium to be non-linear.

### Do consumer prices and precious metal prices have a simple equilibrium relationship?

To assess the long-run hedging properties of gold and silver against inflation, Bampinas and Panagiotidis (2015) analyse a long run dataset using both time-invariant linear cointegration and the time-varying cointegration approach of Bierens and Martins (2010). Their dataset on local-currency gold and silver prices, as well as consumer price indices for the US and UK, runs from 1791 to 2010.

- The authors examine the stationarity of the nominal and real prices of gold and silver, as well as price indices, in both economies using a number of alternative stationarity tests. Although they find that the nominal metal prices and consumer price indices are all nonstationary, test results conclude that
__real (CPI-adjusted) gold and silver prices are stationary over time__, supporting the plausible idea that precious metal prices drift in the long run in line with overall inflation. - The authors formally test for the presence of cointegration by regressing US and UK consumer price indices on the nominal metal prices in a bivariate vector error correction (VECM) model. A VECM is a variant of vector autoregression incorporating the prior deviation of each variable from its estimated equilibrium value in order to model the future drift of this error. The authors find “that
__there is one cointegrating vector between each pair of gold prices and headline inflation in both countries__…[However, ] the evidence for silver prices and headline inflation indicates no long-run relationship for both countries.” - The authors further examine the relationship between gold and silver prices and expected inflation, by using the trend component of consumer price indices, extracted via the Hodrick-Prescott (HP) and Christiano-Fitzgerald (CF) filters to proxy for inflation expectations. Similarly, they find evidence of
__a cointegrating relationship for gold in both the US and the UK__, with the strength of the relationship sensitive to model speciation. No evidence is found for a cointegrating relationship between silver and inflation expectations proxies.

### Investigating more complex types of relations

A time-varying cointegration framework allows for the __smooth adjustment of the equilibrium relationship __through time, and __permits adjustment towards this equilibrium to be nonlinear__.

“Over the last two centuries, the UK and the US have witnessed __policy regime shifts and changes in market conditions__. These events could affect the long-run relationship between precious metals and consumer prices. Furthermore, previous evidence of nonlinearity for gold and silver reinforces the argument for the time-varying approach. For this purpose, we __relax the assumption that the long-run relationship has remained constant through the last two century period__ by employing the time-varying framework of Bierens and Martins (2010), where the cointegrating vectors fluctuate over time.”

There is __strong evidence of a time-varying cointegrating relationship between gold and inflation__. There has also been a significant long-run relationship between CPI and silver, if one allows this relationship to vary overtime.

“In general, for the US there is evidence in favor of time-varying cointegration between gold prices and headline, expected and core measures. Similar results hold for the UK’s gold prices while __strong time-varying cointegration emerges between the UK’s silver price and all price level measures__.”

Lucey et. al. (2017) extend the results of Bampinas and Panagiotidis (2015) to Japan, and to consider PPI inflation as well as data on the money supply. The authors formally test for time variation in the cointegrating relationship, and find evidence for a long run relationship between gold prices and inflation through time. Evidence of time-varying cointegration is found between gold and US CPI for the majority of the period between 1975 and 1995, but no significant cointegration is evidenced between 1995 and 2008. After 2008, however, evidence of a long-run relationship between gold and US CPI rapidly re-asserts itself. A similar overall pattern is seen using PPI as the inflation measure.

### Hedging with platinum and palladium

Bilgin et al. (2020) examine the inflation-hedging properties of white precious metals – silver, platinum and palladium – across eleven countries, including a mix of developed and emerging markets, also utilizing the time-varying cointegration framework.

“Covering a 28-year period across eleven countries, the study finds that __platinum is the most effective long-term hedge__. whiles palladium work better as a hedge against short-term dynamics. Findings suggest that platinum and palladium are more reliable inflation hedges than silver because of their importance for industry…__Platinum and palladium outperform silver in an inflationary__ environment, thereby qualifying the two white precious metals as potential alternatives to classical inflation hedgers and also tools to further diversify an investment portfolio.”

Plots of the trace-test statistic for the presence of cointegration between inflation and all three metals are reproduced below, scaled relative to the critical value. A test statistic below one indicates evidence of a cointegrating relationship.

### A quantile analysis of inflation hedging with gold

A complimentary approach to estimate the relationship between precious metal prices and inflation is to allow the relationship to vary across the quantiles of both variables: that is to say, the __hedging properties of gold may be stronger (weaker) under certain inflation regimes__ and certain gold price regimes than under others.

Shahzad et. al. (2020) assess the inflation hedging properties of gold with respect to inflation in China, India, France, Japan, the UK and the US. They employ the quantile-on-quantile (QQ) approach of Sim and Zhou (2015), which __generalizes conventional quantile regression to allow the effects of each quantile of one variable upon the conditional quantiles of another variable to be examined__. Their approach therefore offers potentially greater insight vs. traditional quantile approaches – which only allow for the effect of one variable to differ across quantiles of another variable.

The charts below plot estimated slope coefficients from the QQ analysis on the vertical axis, with quantiles of gold and inflation on the horizontal axes. Overall, there is considerable heterogeneity in the gold-inflation slope coefficient across quantiles of both gold and inflation, suggesting that __the link between inflation and gold prices is highly contingent on the level and sign of inflation shocks__. There is are also considerable differences in the patterns of observed slope coefficients for different countries.

The authors next combine quantile and non-parametric Granger causality techniques to examine whether causal inference can be drawn from the relationship between the two variables. They __test for Granger-causal relationships from CPI inflation to both the mean and the variance of the gold price series__. Although there is considerable heterogeneity between different countries, and between causality test results with respect to the mean and variance of gold prices, the __results generally show stronger evidence of a causal relationship for moderate quantiles__:

“More precisely, for the first order causality (or causality-in-mean), there is evidence of a causality from the CPI growth rate to gold price growth at the middle quantiles. The CPI growth rate for China Granger causes the gold price growth in the average quantiles (from 0.50 to 0.75), indicating that inflation has a strong predictive power of changes in the gold prices around the middle quantiles. The result also reveals that changes in the low- and high-quantile ranges for the CPI are not associated with the gold markets, supporting the decoupling hypothesis. As for France, the causal flow (in both the mean and the variance) is evident across all the quantiles. This result indicates that gold plays a strong hedging role against inflation. The causality relationship between gold growth and the growth rate of CPI is quite similar for China, Japan and the UK. In fact, the causality in the first and second order from the growth rate of CPI to the gold price growth is significant for all quantiles, with the exception of the lowest and highest (or the extreme) quantiles, underlying the crucial role gold plays to hedge the inflation in those countries.”

### References:

Bierens, H.J. and Martins, L.F., 2010. Time-varying cointegration. *Econometric Theory*, pp.1453-1490.