(Phillips et al., 2015a; 2015b; Phillips and Shi, 2020) develop a Generalized Sup Augmented Dickey-Fuller (GSADF) method to test for the presence of multiple bubbles and a recursive backward regression technique to date the bubble origination and termination. GSADF tests rely on a recursive series of right-tailed ADF tests where, instead of fixing the starting point of the recursion on the first observation, the window of observations changes its sample size by changing the starting and the endpoints of the recursion on a feasible range of windows (see Figure 3).

Let us consider the following asset pricing equation: P t = ∑ i = 0 ∞ 1 1 + r f i E U t + i + B t , (1) where P t is the price of the asset, r f is the risk-free interest rate, U t represents the unobservable market fundamental factors, and B t is the bubble element. Since we are considering a commodity (lithium) price instead of equity prices, we have excluded the dividend term that is commonly encountered in Eq. 1. P t f = P t − B t is called the market fundamental, and B t satisfies the following property: E t B t + 1 = 1 + r f B t (2)

When B t presents the dynamics described in Eq. 2, the asset price is said to be explosive. When the observable fundamentals are at most I Eq. 1, empirical evidence of explosive behavior in asset prices may be used in order to infer the existence of financial exuberance or price bubbles. Naturally, model specification is important for estimation. It has potential impacts on the test critical values, whether intercepts, deterministic trends, or trend breaks are included (or not) in the alternative hypothesis. Other authors include a martingale null with a negligible drift (Phillips et al., 2014), which is empirically realistic over long time periods. A model of this type can be written as: P t = d T − η + θ P t − 1 + ε t , ε t ∼ i i d 0 , σ 2 ) , θ = 1 , (3) where d is a constant, T is the sample size, and the parameter η regulates the magnitude of the intercept and drift as T → ∞ . Solving for P t in Eq. 3 leads to: P t = d t T η + ∑ j = 1 t ε j + P 0 (4) where d t T η corresponds to a deterministic drift. When η >   0 , the drift is small relative to a linear trend; when η > 1 2 , it is relatively small with respect to the martingale element of P t . When η < 1 2 , T − 1 / 2 P t behaves asymptotically like a Brownian motion with drift. Specifically, for the test used in this study, we consider the case of η > 1 / 2 , in which the order of magnitude of P t is the same as that of a pure random walk.

The model specification in Eq. 4 is usually complemented with temporary dynamics in order to test for exuberance, as in standard ADF unit root testing for stationarity. The recursive approach involves a rolling window ADF style regression. Specifically, the rolling window regression sample starts from the r 1 t h fraction of the sample T and ends at the r 2 t h fraction of the sample, where r 2 = r 1 + r w , and r w > 0 is the window size in relative terms.

The empirical regression model takes the following form: Δ P t = α ^ r 1 . r 2 + β ^ r 1 . r 2 P t − 1 + ∑ i = 1 k ψ ^ r 1 . r 2 i Δ P t − i + ε ^ t (5) where k is the (temporary) lag order. The sample size in the regressions is T w = ⌊ T r w ⌋ , where ⌊ . ⌋ is the floor function. The ADF statistic based on this regression is denoted by A D F r 1 r 2 . Basically, the GSADF consists of a repeated set of ADF regressions as in Eq. 5, conducted on subsamples of the data in a recursive fashion. This test allows the starting point in Eq. 5 to change within a feasible range from r 2 − r 0 . (Phillips et al., 2015a) and defines the GSADF statistic as the largest ADF statistic in a double recursion over all possible ranges from r 1 and r 2 : G S A D F r 0 = sup r 2 ∈ r 0 , 1 r 1 ∈ 0 , r 2 − r 0 A D F r 1 r 2 (6)

Based on extensive simulations, ref (Phillips et al., 2015a; Phillips et al., 2015b) recommend a rule for choosing r 0 that is based on a lower bound of 1% of the full sample r 0 = 0.01 + 1.8 / T .

The bubble detection test is based on a double recursive test procedure, called backward sup ADF (BSADF) test, which is designed to enhance the identification accuracy of the original statistic. Specifically, the BSADF test performs a sup ADF test on a backward expanding sequence in which the endpoint of each sample is fixed at r 2 and the start point varies from 0 to r 2 − r 0 , as shown in Figure 3. The corresponding ADF statistic sequence is A D F r 1 r 2 r 1 ϵ 0 , r 2 − r 0 . The backward SADF statistic is written as: B S A D F r 2 r 0 = sup r 1 ϵ 0 , r 2 − r 0 A D F r 1 r 2 (7)

The bubble origination date ( ⌊ T r ^ e ⌋ ) is established as the first observation whose BSADF statistic is higher than the critical value (Phillips et al., 2015a).of the test. The ending of a bubble is dated as the first observation after ⌊ T r ^ e ⌋ + δ ⁡ log T whose BSADF statistic falls under the critical value. For an exuberance episode to be considered as a bubble, its duration should exceed a minimal period represented by δ ⁡ log ⁡ ⁡ T , where δ is a predetermined parameter that refers to the minimal duration of the bubble.

Formally, the origination and the ending points of a bubble are estimated according to the following formulae: r ^ e = inf r 2 ϵ r 0 , 1 r 2 : B S A D F r 2 r 0 > s c v r 2 β T (8) r ^ f = inf r 2 ϵ r ^ e + δ ⁡ log T T , 1 r 2 : B S A D F r 2 ( r 0 < s c v r 2 β T (9) where s c v r 2 β T is the 100 1 − β T % critical value of the sup ADF measure based on ⌊ T r 2 ⌋ observations. The GSADF procedure employs the backward sup ADF test for each r 2 ϵ   r 0 , 1 and its inferences are based on the sup value of the backward sup ADF sequence B S A D F r 2 ( r 0 r 2 ϵ r 0 , 1 . Therefore, the GSADF statistics can be written as: G S A D F r 0 = sup r 2 ϵ r 0 , 1 B S A D F r 2 r 0 (10)

Novel to the literature, we propose to measure the level of synchronization between different lithium market price’ bubbles and potentially between any other pair of commodities or assets, by means of the following concordance statistic and assuming there is at least one bubble period: I ^ = ∑ t = 1 T S x t S y t / ∑ t = 1 T S x t (11)

For ∑ t = 1 T S x t > 0 , where x t and y t are the series of prices of two market assets, and S x t and S y t are binary indicators that take the value of 1 and 0 depending on whether the market is in a bubble phase or not, respectively. The concordance index reads as the proportion of time that the two series were in a bubble phase, relative to the number of periods the first asset, x t , was in a bubble phase. A value of one indicates that every period the first market was in a bubble, the second market was in a bubble too.

When ∑ t = 1 T S x t = 0 , I ^ ≡ 0 . Thus, a value of zero of the concordance statistic indicates that the two markets were never in a bubble at the same time.

We use lithium contract prices for geographic regions retrieved by Benchmark Metals Inc., available at Bloomberg. Such contracts include negotiation prices of lithium carbonate and lithium hydroxide, selected according to their current and future relevance for the electric vehicle (VE). We consider: Asian lithium carbonate, hydroxide-Cost, Insurance and Freight (CIF) Swaps- and hydroxide-Ex Works (EXW) Swap-; European lithium carbonate and lithium hydroxide CIF swaps, North American lithium carbonate and lithium hydroxide CIF swaps, and South America lithium carbonate-Free on Board (FOB) Swap-. Our sample spans January 2009 to December 2022 and consists of monthly observations of the contract prices (168 observations). Table 1 shows lithium price descriptive statistics.

All the results were obtained using statistical software R, using the psymonitor package developed by Phillips et al. (2018) and Phillips and Shi (2020).

Our findings indicate that the remarkable price surge witnessed in all lithium markets between 2016 and 2018 might be attributed to speculative dynamics and the presence of bubbles. These bubbles may have emerged as a result of market overreaction to fundamental factors, particularly the increased demand for lithium in China driven by the development of electric vehicles (EVs). The duration and persistence of these bubbles vary across different geographical locations and depending on whether the market focuses on hydroxide or carbonate variants of lithium (refer to Figure 3). Furthermore, our results provide clear evidence that lithium markets currently exhibit mildly explosive dynamics characteristic of bubbles.

On the left of Figure 4, the GSADF statistic estimated as in Eq. 11 is plotted. Alongside the statistic, we present the critical values at 90%, 95%, and 99% of confidence (dotted lines). Every month that the GSADF statistic exceeds the critical value, lithium is said to exhibit a price bubble, i.e., to follow mildly explosive dynamics. The right column of Figure 2 shows the lithium contract price path and grey areas correspond to bubble phases at 99% level of confidence.

In the Asian market, the three contracts in our sample exhibited explosive dynamics simultaneously; such explosive dynamics are mostly concentrated between 2016 and 2018. For instance, the lithium carbonate price shows an explosive behavior from November 2015 to April 2018 with a total duration of 30 months. In the case of lithium hydroxide EXW, the explosive dynamics took place from January 2016 to December 2017, lasting 24 months. Asia lithium hydroxide exhibits explosive dynamics from February 2016 to March 2018. For all Asian lithium prices, a bubble is detected starting in September 2021 and extending to the end of the sample.

In the European lithium market, both lithium carbonate and lithium hydroxide prices exhibit explosive dynamics with similar duration, albeit in different periods. The lithium carbonate price shows an explosive path from February 2016 to July 2018 (30 months), while lithium hydroxide shows explosiveness from March 2016 to December 2017 for a total 22 months. Both markets show evidence of a bubble from December 2021 until the end of the sample.

Lithium carbonate and lithium hydroxide prices also exhibit explosive paths in the North American market. For lithium carbonate, a bubble lasting 31 months was observed between January 2016 and July 2018. The lithium hydroxide price showed explosive behavior from January 2016 to September 2018 (33 months). The two markets show bubbles starting in October 2021 and extending until the end of the sample.

With respect to the South American lithium market, we analyze the dynamics of lithium carbonate. This price exhibits two bubble periods; the first period extends from January 2016 to October 2018, lasting 34 consecutive months, and the second period of explosive price behavior starts in December 2021 and lasts until December 2022 (end of sample).

In general, lithium prices in all the markets studied exhibit a sustained explosive pattern from the beginning of 2016 (or even late 2015) until year 2018. However, the persistence of explosive dynamics varies between markets and within types of lithium. The longest duration of a lithium bubble was recorded in the South American market (34 months for lithium carbonate). All markets show evidence of a bubble at the end of the sample (almost always starting in October 2021).

Note: On the left of the figure are plotted the GSADF statistics estimated according to Eq. 11, and the test’s critical values at 90%, 95%, and 99% of confidence. When the value of the statistic is greater than the value of the associated critical value, the lithium price is said to experience a bubble phase. Right column: The line corresponds to the lithium contract prices. The grey area corresponds to the period in which, according to the GSADF statistic (left column), the lithium price presented explosive dynamics at 99% confidence level.

In Table 2, we present the concordance statistic between the bubbles of the 8 lithium markets in our sample. As can be seen, the bubbles identified in all 8 markets exhibit a high level of synchronization. There are several pairs for which the concordance statistic reaches 1, meaning that the bubbles identified for the market indicated in the first column of Table 2 occurred at the same time as the bubbles identified in other markets indicated in the first row of the table. For instance, Asia hydroxide bubble coincided 100% of the time with a bubble in Asia Carbonate and in Europe Hydroxide, and 82% of the time with a bubble in Asia EXW. However, the table is not symmetric. Using the same example, we note that the Asia carbonate bubble intercepts with the Asian Hydroxide bubble 91% of the months and with Asian EXW Hydroxide 82% of the times. This occurs because the bubbles do not have the same duration. The minimum value in the table is 57% between Europe Carbonate and Europe Hydroxide, meaning that all markets exhibit a high degree of bubbles’ synchronization.

We test for the presence of bubbles in some global stocks and commodities markets that could serve as investment alternatives in the event that a stabilization fund for the lithium price is established. The analysis is carried out for the same sample period as before. For stock markets, we examine the price dynamics of the American, European and Asian stock markets through the following reference price indices: S&P 500 index, FTSE100 and Eurostock 50 indices, and the Asian Nikkei 225, Hong Kong Hang Seng, and TOPIX indices. In the commodity markets, we analyze exuberant price dynamics of benchmark oil prices, namely, the West Texas Intermediate (WTI) and the Brent blend. We also test for explosiveness of gold and silver spot prices under the assumption that such metals can serve as value reserve in a portfolio.

Our estimates presented in Figure 5 indicate that during the sample period the stock markets indices included in our sample did not experience bubbles, contrary to lithium price dynamics described in the previous section. In terms of commodities, we document explosive behavior for short periods, which do not coincide with explosive price dynamics in any of the lithium markets analyzed before. For instance, the BRENT oil price presents a bubble from November 2014 to January 2015, the gold spot price exhibits explosive behavior from July 2020 to August 2020, and the silver spot price in April 2011.

Only in the case of European hydroxide, which experienced an overlapping bubble with the short bubble identified in gold, was the concordance statistic different to zero (equal to 4.35%). In all other cases, the synchronization of bubbles from the perspective of lithium markets was estimated at zero.

Note: On the left of the figure are plotted the GSADF statistics estimated according to Eq. 11, and the test’s critical values at 90%, 95%, and 99% of confidence. When the value of the statistic is greater than the value of the associated critical value, the lithium price is said to experience a bubble phase. Right column: the line corresponds to the lithium contract prices. The grey area corresponds to the period in which, according to the GSADF statistic (left column), the lithium price presented explosive dynamics at 99% confidence level.

Our contribution is related to a debate that took place a few years ago in the energy field, and which has been revived in recent years following the significant decline in lithium prices observed from 2018 onwards. Debate that has regained relevance during the second half of 2021, when the new committed political global efforts to fight climate change have been accompanied by a surge in the price of lithium (see Figure 1). On the one hand, a branch of studies attributed a lithium price surge in the mid-2010s to lithium shortages, supply-demand imbalances, and production delays. On the other hand, speculative investors and the appearance of market bubbles have also been blamed for lithium’s price booms. Within the former set of advocates, several questions have been raised about lithium reserves and availability. Such questions involve the possibility of a global lithium shortage, with a supply unable to match a growing demand. The more popular reasons claimed by analysts to explain the rapid price increase include a supply squeeze of the lithium exported to China, growing long-term demand from start-up and established EV manufacturers, and a growing market for portable electronic devices (Miedema and Moll, 2013; Narins, 2017; Sun et al., 2017; Speirs and Contestabile, 2018). In the same vein, it has also been stated that this price surge was due to a consumption–production imbalance (Martin et al., 2017), following a rapid consumption growth of lithium battery applications.

However, the possibility of a lithium shortage has been ruled out by other authors (Jaskula, 2015). According to this view, lithium is readily available on Earth and, furthermore, the world could triple its production from current levels and still have 135 years of supply available using solely known reserves. An alternative explanation suggests the reporting role of the financial press (The Economist, 2016a; The Economist, 2016b; Forbes, 2016), which named lithium as the hottest commodity and documented that its demand was rising spectacularly as well as the demand for lithium-related securities, offering higher than average returns to investors.

Results in Section 4 show that there were bubbles in the 8 lithium prices considered here. Moreover, these bubbles were synchronized with each other, meaning that bubbles across various lithium markets tend to emerge (and burst) simultaneously. This is very inconvenient from a risk management perspective because risk is poorly diversified when simultaneous bubbles originate and collapse in multiple assets or inputs at the same time. Unfortunately, the economics profession has little to say about risk-management when dealing with market bubbles, and even less if such bubbles are highly synchronized with each other. The few advances of the discipline in this direction have focused on trading and on generating models for prediction of market corrections and crashes (Greenwood et al., 2019), but have said little about how to hedge against the risk of bubble inflation and bursting. The literature has traditionally, and consistently, relegated policy action in the face of bubbles to “wait until the market corrects itself”. This was clearly the case after the dot.com bubble of technological firms that ended in 2002 in the United States NASDAQ market. However, the Global Financial Crisis, and the dramatic bursting of the mortgage market bubble that preceded the crisis, pointed to the greater dangers of the “cleaning up the mess” approach only after a bubble has burst. Following the financial crisis, there have been some attempts to provide the means to understand and manage financial bubbles when they appear, mostly from a macroeconomic perspective. More in line with the scope of our study, one of the few studies that has examined those characteristics which make a firm more resilient in the presence of bubbles (Brunnermeier et al., 2020) focuses on financial institutions. It seems that larger banks, a stronger maturity mismatch and higher loan growth tend to make financial institutions, and hence the financial system, more vulnerable to systemic risk as a consequence of market bubbles. Unfortunately, such attributes do not extrapolate to lithium producers and consumers, who belong to a different industry which is considerably less cyclical than banking.

Our approach is different. We stress that the main issue regarding the presence of bubbles in lithium markets is related to the high degree of uncertainty that accompanies their inflation and bursting. Uncertainty is known to reduce investment (Bloom, 2014). When in an uncertain environment, firms optimally decide to delay investment until after uncertainty has passed. In the case of lithium, such a strategy is suboptimal from a societal perspective, given the large implications that a lithium shortage would have for the transition of the transportation sector to a low-carbon technology, especially in Europe, China and the United States. One way to reduce the uncertainty related to lithium prices and future cash flows of lithium producers is by setting minimum prices in advanced for buying lithium, by means of derivative contracts (e.g., options). These minimum prices should be high enough to cover investment expenditures by lithium producers, which are needed to guarantee an increasing supply of lithium in the forthcoming decades. Moreover, in countries relying on Li-ion batteries for their energy transition, stabilization funds could be established that would be used in case spot prices ended up being lower than prices projected by lithium producers. These funds could, in such an event, pay the market differential between the observed spot price at the time of delivery and the contracted price of lithium set at the time of investment in exploration and extraction.

The important question remains as to where these funds should be located. In this case, instead of resorting to a traditional portfolio optimization perspective to solve the problem of capital allocation, we explore some traditional investments, which have historically depicted low synchronization with bubbles in the lithium markets. The general idea is to reduce the presence of simultaneous bubbles in the portfolio (treating lithium as an asset), given the inherent difficulty in forecasting in real time when a bubble will end (Greenwood et al., 2019). In this case, our results highlight the lowest synchronization of bubbles in lithium markets with all traditional portfolios, including stocks, precious metals and oil. The kind of analysis conducted here does not aim to be comprehensive; indeed, other market assets may (and must) be explored. Ideally, where public funds and capital buffers are to be located depends on the specific stakeholder’s asset-liability structure. Our aim is to provide a way of conducting this crucial part of techno-economic analyses which has so far been overlooked.