metadata: authors: 0: author: Calvo-Gonzalez,Oscar
1: author: Shankar,Rashmi
2: author: Trezzi,Riccardo
count: World
docna: 0: docna: Are commodity prices more volatile now ? a
            long-run perspective
docty: Policy Research Working Paper
subtopic: Primary Metals,Macroeconomic Management,Inequality,Armed Conflict,Commodity Risk Management
teratopic: Private Sector Development,Macroeconomics and Economic Growth,International Economics and Trade
abstracts: cdata!: Soaring commodity prices in 2007 and
            2008 raised concerns that volatility was also rising, which
            would have implications for welfare and therefore for the
            design of public policy interventions. The literature
            focuses on trends in commodity prices rather than their
            volatility characteristics. This paper contributes by
            examining commodity price volatility with a newly compiled
            monthly panel dataset on 45 individual commodity prices from
            the end of the 18th century until today. The main
            conclusions are: the timing and number of breaks in
            volatility vary considerably across individual commodities,
            cautioning against generalizations based on the use of
            commodity price indices; the three most significant breaks
            common to most commodities are the two world wars and the
            collapse of the Bretton-Woods system; and structural breaks
            marking increased price volatility are followed by breaks
            marking declines in volatility so that there is no upward or
            downward trend in volatility over time.
repnme: repnme: Are commodity prices more volatile now ? a
            long-run perspective
display_title: Are commodity prices more volatile
            now a long-run perspective
listing_relative_url: /research/2010/10/12916918/commodity-prices-more-volatile-now-long-run-perspective
topicv3: Price Volatility m1326059 1150,Poverty m1326687 695,Political Violence and War m1327310 2462,Copper m1503516 2934,Commodity and Resource Prices m1503849 3034
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Private Sector Development,Macroeconomics and Economic Growth,International Economics and Trade
no_of_pages: 35
author_keys: 0: author_key: 915932
1: author_key: 168347
2: author_key: 1006503
model_extractions: WPS5460 Policy Research Working Paper 5460 Are Commodity Prices More Volatile Now? A Long-Run Perspective _Oscar Calvo-Gonzalez Rashmi Shankar Riccardo Trezzi_ The World Bank Latin America and the Caribbean Region Poverty Reduction and Economic Management Department Economic Policy Unit October 2010
Policy Research Working Paper 5460

# **Abstract**

Soaring commodity prices in 2007 and 2008 raised concerns that volatility was also rising, which would have implications for welfare and therefore for the design of public policy interventions. The literature focuses on trends in commodity prices rather than their volatility characteristics. This paper contributes by examining commodity price volatility with a newly compiled monthly panel dataset on 45 individual commodity prices from the end of the 18th century until today. The main conclusions are: the timing and number of breaks in volatility vary considerably across individual commodities, cautioning against generalizations based on the use of commodity price indices; the three most significant breaks common to most commodities are the two world wars and the collapse of the Bretton-Woods system; and structural breaks marking increased price volatility are followed by breaks marking declines in volatility so that there is no upward or downward trend in volatility over time.

This paper—a product of the Economic Policy Unit, Poverty Reduction and Economic Management Department, Latin America and the Caribbean Region—is part of a larger effort in the department to provide policy relevant research on topics of interest to the region. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at rshankar@worldbank.org and ocalvogonzalez@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Are Commodity Prices More Volatile Now? A Long-Run Perspective**

Oscar Calvo-Gonzalez, Rashmi Shankar, Riccardo Trezzi JEL No.: F14, C59, E32 Key words: International commodity prices, volatility, structural breaks The authors would like to thank David Jacks, Emily Sinnott, John Nash, Cesar Calderon, and participants at the Authors' Conference for the Regional Flagship Study on Commodities for comments provided at various stages during the preparation of this paper that have been invaluable to its development. All remaining errors are fully attributable to the authors. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they represent.
# **1. Introduction and Motivation**

On July 11, 2008 the spot price of West Texas intermediate crude oil peaked at US$ 146 per barrel, exactly double the price a year earlier. Since then, oil prices bottomed at US$30 in December 2008, rebounding to around US$ 70 as of the time of writing. Such see-saw movements have not been confined to oil only. In 2008 large increases were also recorded for foodstuffs, metals, and commodities in general. The “commodity boom” was everywhere in the news and in policymakers’ agenda. The concern was not only about the elevated price of commodities, but also that these prices had become more volatile.<sup>1</sup> Some analysts, including the OECD, argued that this higher commodity price volatility seemed to be driven by structural determinants.<sup>2</sup> The issue of rising commodity price volatility is policy relevant. Poor countries with production and trade structures concentrated on commodities are vulnerable to price swings. The perceived welfare effects of variable commodity prices have inspired public policy interventions in developed countries as well.<sup>3</sup> Even the beneficiaries of higher commodity prices, such as farmers, have expressed concerns that higher volatility renders hedging mechanisms ineffective.<sup>4</sup> Their complaint was that options had become so expensive due to elevated levels of volatility and hence risk, so that using options as a hedge was no longer financially viable. In general, a large number of policies – price supports, buffer stocking, and producer and consumer subsidies – have been rationalized on the basis that smoothing commodity price volatility away carries significant welfare gains.

While there is a large literature focused on the trend in price level, stemming from the Prebisch-Singer hypothesis of a secular decline in the relative prices of primary products,

> 1 International Institute for Sustainable Development 2008 argued that “[...]in the past 30 years, there have been as many price shocks across the range of commodities as there were in the preceding 75 years” _Boom or bust: how commodity price volatility impedes poverty reduction, and what to do about it”,_ IISD, January 2008.

> 2 OECD-FAO (2008) Agricultural Outlook 2008-2017 discussed at length permanent factors that may increase volatility and underlined how Least Developed Countries could be negatively affected in an era of “high commodity prices and high price volatility, _”_ pg. 4.

> 3  For example, the EU’s Common Agricultural Policy, the Canadian Wheat Board, and US implicit agricultural price support policies.

> 4 “Price Volatility Adds to Worry on US Farms,” New York Times article on April 22, 2008.

2
volatility characteristics of commodity prices have attracted less attention. In this paper, we therefore address the following question: has commodity price volatility increased? We do this by exploiting a newly compiled unbalanced panel dataset on 45 individual commodity prices spanning the 1784-2009 period at a monthly frequency.

# **2. Literature Review**

Ever since Prebisch (1950) and Singer (1950), a vast literature has grown around the issue of identifying a secular trend in commodity prices. This research has been mainly concerned that commodity prices tend to decline relative to the price of manufactures with obvious implications for the primary producers.<sup>5</sup> In contrast, the literature on the volatility of commodity prices and its public policy implications is relatively small. This research is mainly focused on understanding how commodity price volatility affects income volatility, especially in poor countries (Koren and Tenreyro (2007)), among others). Other authors have been concerned with how commodity price volatility generates instability in international markets (Blanford (1983), Heifner and Kinoshita (1994) among others).

While mainly concerned with identifying price cycles – booms and slumps – Cashin and McDermott (2002) also test to see if variability in prices is higher or lower across cycles. Using The Economist’s index of industrial commodity prices over the period 1862 – 1999, they find evidence of a ratcheting up in the variability of commodity price movements around 1899 and then again in the early 1970s.<sup>6</sup> The finding of higher variability in commodity prices after the end of the Bretton Woods era is in line with hypotheses of a link between nominal (and real) exchange rates and the volatility of dollar denominated commodity prices Chu and Morrison (1984), Reinhart and Wickham (1994), Cuddington and Liang (1999). Comparing three different datasets<sup>7</sup>

> 5 Interest about a possible negative long-term trend in commodity prices has occupied development economic literature since the late 1940s. For instance in Prebisch (1950) and Singer (1950), Grilli and Yang (1988), Cuddington and Urzua (1989), Cuddington (1992), Powell (1991), Reinhart and Wickham (1994). 6  For annual data, Cashin and McDermott define large booms as a sequence of generally increasing prices that have had a price movement of at least 25 percent over the phase, and large slumps as a sequence of generally decreasing prices that have had a price movement of at least 25 percent over the phase.

> 7 The datasets are the following: (1) the annual data set of Grilli and Yang from 1900 to 1992, (2) Boughton’s dataset with annual observations from 1854 to 1990, (3) the IMF’s _International Financial Statistics_ (IFS) which covers the post World War II period with monthly observations.

3
and using the methodology in Eichengreen (1994) to identify exchange rates regimes, Cuddington and Liang (2003) find that the relative price of primary commodities in terms of manufactured goods exhibits greater volatility since the early 1970s, a period characterized by an increasing number of flexible-exchange rate regimes. Mitchell (1987) presented the idea that increased trade, capital flows, policy shocks to macroeconomic variables and exchange rate uncertainty affect agricultural commodity prices.

Moledina, Roe, and Shane (2004) find little evidence for higher volatility post-1971, once predictable components are removed from the “classic” measure of volatility (the unconditional standard deviation or the coefficient of variation<sup>8</sup> ). Moreover, they show no statistical evidence for either a positive or negative trend in median volatility. Only three of the twelve commodities in their sample (bananas, coffee, and wheat) show some increase in volatility over the sample period. They argue that the welfare gains from eliminating commodity price volatility are therefore tiny, at less than one percent of total consumption.

One lesson from Moledina _et al_ (2004) is that the absence of a common trend across commodity prices calls for a need to study factors underlying commodity price volatility separately in each market. This was also highlighted by Leon and Soto (1995), who had analyzed the long-run dynamics of the price of the 24 most traded commodities over the 1990 – 1992 period. They tested for the presence of unit roots in the series, allowing for endogenously determined structural breaks. The results show that 15 of the 24 commodity prices in their sample exhibit a negative trend, six are trendless, and three show a positive trend<sup>9</sup> .

Closest to this paper in spirit is Jacks, O’Rourke and Williamson (2009), who also examine commodity prices over a long time span. They define volatility as the standard deviation of price changes over a given period and use monthly observations on local market prices (to account for the impact of tariffs and embargoes) for four broadly defined commodity indices. They use the standard UNCTAD classification: all food

> 8 See Offutt and Blandford (1981) for a list of different single variable measures based on the standard deviation. Moreover, see Kroner, Kneafsey, and Claessens (1993) for a “classical” approach using the standard deviation of price changes.

> 9 The Cusum Break Test for TS models shows the following breaks: Coffee 1945, Maize 1920, Palm Oil 1985, Rice 1920, Sugar 1922, Timber 1985, and Tin 1985.

4
(AF), agricultural raw materials (ARM), minerals, ores and metals (MOM) plus a fourth group for manufactures or final good (FG).

We provide below a review of the existing literature on commodity prices volatility.

|**Author**|**Research Question**|**Data**|**Methodology**|**Results**|
|---|---|---|---|---|
|Moledina A., Roe|The paper tries to determine|Monthly prices (1957-|GARCH (or ARIMA)|The paper attributes most of|
|L., Shane M.|the most appropriate measure|2001) for selected|model fitted to|the volatility in commodity|
|(2004)|of commodity prices volatility<br>and investigates the presence<br>of a linear time trend in the<br>conditional volatility series.|agricultural<br>commodities from<br>IMF’s_IFS_. CPI data<br>from Bureau of Labor<br>Statistics are used to<br>deflate each commodity<br>series.|compute conditional<br>volatility.|prices to macroeconomic and<br>political factors. Moreover,<br>the median volatility over<br>time for all commodities does<br>not show consistent increases<br>or decreases.|
|Cuddington J.T.,<br>Jerrett D. (2008)|Do metal prices exhibit any<br>long-term upward or<br>downward trends? Is there<br>evidence of a strong super-<br>cycle component for each<br>series? Is there any strong co-<br>movement of the super-cycle<br>components? How<br>pronounced are the shorter<br>cycles?|Annual data series (in<br>some cases from 1850)<br>on the LME-traded<br>nonferrous metals from<br>Heap (2005). US CPI<br>(2006=100) used to<br>deflate the series.|Band-pass filters<br>developed by Baxter<br>and King (1999) and<br>Christiano and<br>Fitzgerald (2003).|Considerable evidence of<br>three past super-cycles in real<br>metal prices. Moreover it<br>finds evidence for high<br>correlation of the six LME<br>metal super-cycles.|
|Jacks S., O’Rourke|Has commodity price|Monthly local city|The paper presents|No evidence of an increase of|
|K.H., Williamson|increased over time? Have|prices (UNCTAD|descriptive statistics|commodity prices volatility|
|J.G. (2009)|commodities always shown<br>greater price volatility than<br>manufactures? Does market<br>integration breed more or less|classification) from<br>different sources,<br>including Bezanson<br>(2005), Posthumus|of a selected measure<br>of volatility. Prices<br>volatility is defined as<br>the standard deviation|though time. It also<br>concludes that higher<br>commodity price volatility<br>compared to manufactures|
||commodity price volatility?|(1946), Friis and<br>Glamann (1958), Gayer,|of the price ratio.|has been a constant since 18<sup>th</sup><br>century. It finds evidence|
|||Rostow, Schwartz||that economic isolation has|
|||(1953), IMF and<br>UNCTAD.||been associated with higher<br>commodity price volatility.|

5
|Cashin P.,|The paper addresses two|Real annual data of the|Following Watson|No evidence of a break in the|
|---|---|---|---|---|
|McDermott C.J.<br>(2001)|research questions: what is the<br>empirical behavior of<br>commodity prices? Are there<br>any changes in the variability<br>of commodity prices and in<br>the trend growth of prices over<br>time?|nominal industrial<br>commodities price index<br>(dollar based), deflated<br>by the GDP deflator of<br>the United States over<br>the period 1862-1999.|(1994) the paper<br>applies two<br>econometric tests on a<br>“peak-trough”<br>analysis to determine<br>the length of a cycle<br>and its statistical<br>significance.<br>Descriptive statistics<br>complement the<br>analysis.|long-run trend decline in<br>commodity prices. Evidence<br>of a ratcheting up in the<br>variability of price<br>movements. The amplitude<br>of price movements increased<br>in the early 1900s, while the<br>frequency of large price<br>movements increased after<br>the collapse of the Bretton<br>Woods regime of fixed<br>exchange rates.|
|Cuddington J.T.,<br>Liang H. (2003)|The study investigates<br>differences in real primary<br>commodity price volatility<br>across fixed and flexible<br>exchange rate regimes.|The paper combines<br>three datasets: Grilli and<br>Yang (1988), Boughton<br>(1991) and IMF’s_IFS_.<br>The paper examines a<br>_real_commodity price<br>index, defined as the<br>ratio of the chosen<br>nominal commodity<br>index deflated by a<br>manufacturing unit<br>value (MUV) index.|ANOVA tests are<br>performed on long-<br>run data to test equal<br>variance across fixed<br>and flexible exchange<br>rate periods. Dummy<br>variables in a<br>(T)GARCH (1,1)<br>framework are used to<br>test the presence and<br>persistence of a<br>volatility shock.|Strong evidence supporting<br>the conjecture that the<br>flexible exchange periods<br>have been associated with<br>higher real commodity price<br>volatility than the fixed<br>exchange periods.|
|Leon J., Soto R.<br>(1995)|The paper revises the long and<br>short run time series structure<br>of commodity prices in order<br>to answer the questions of the<br>secular decline and the long-<br>run persistence of shocks.|Monthly prices of the<br>twenty-four most-traded<br>commodities in 1900-<br>92.|The paper applies the<br>non-parametric<br>estimator of<br>persistence proposed<br>by Cochrane (1988<br>and 1991) and<br>extended by Lo and<br>McKinley (1989) and<br>Chow and Denning<br>(1993).|15 of the 24 commodity<br>prices have negative trends, 6<br>are trendless and 3 exhibit<br>positive trends implying that<br>Prebisch-Singer hypothesis<br>holds for most commodities.<br>Evidence suggests that there<br>may be substantial room for<br>stabilization and price<br>support mechanisms for most<br>commodities.|

6
Here, the question of whether commodity price volatility has increased over time is addressed with analytical rigor and at a disaggregated level. We use a unique, newly compiled dataset of 45 individual commodity prices and five commodity price indices at a monthly frequency. Two econometric tests are applied for identifying structural breaks in GARCH-type processes in order to provide a robustness check and these are described below.

# **3. Data**

For this paper we use a newly compiled dataset which covers 45 individual commodities and 5 commodity price indexes. We use a monthly unbalanced panel of observations from Global Financial Data (GFD) covering the period 1784 – 2009. We take a pragmatic approach as to what constitutes a “commodity” and take all “commodities” included in the GFD dataset as our subject of study. We use data from GFD as it is the most comprehensive source, verifying that the price data is consistent with that from alternative sources (World Bank, IMF, and UNCTAD) for any overlapping commodity and time period. The details of the dataset can be found in Table 1.

7
|Group|Sub-group N|o.<br>Commodity|Additionaldescription (ifany}|Units|Monthlydata<br>|Source|
|---|---|---|---|---|---|---|
||||||available since||
|Enerzy||1 Coal||UssTm|Jan-1932|GFD|
|||2 Crudepetroleum|West Texas Intermediate|UsSbarrel|Jan-1860|GFD|
|Food|Beverages|3Cocoa||Uss/Tm|Jan1817|GFD|
|||<br>4 Coffee|Brazil SantosArabica|UScenta'lb|<br>Jan-190)|GFD|
|||5 Tea<br>||UScentsTh<br>|Jan-1861<br>|GFD<br>|
||Fats and<br>|6 Copra<br>|Philippinescopra<br>|UsS'Tm<br>|Jan-1925<br>|GFD<br>|
||oils|7 Corn oil|Wet mill, Chicago|UScents‘pound|Jul-1924|GFD|
|||§ Cottonseed oil||UScents'lb|Anz-1909|GFD|
|||° Lard|Average wholesale price|UScents'lb|Jan 1859|GFD|
|||10 Sorbean oil||UScents'lb|Jan-1911|GFD|
|||1]Soybeans||USS/bushel|Sep-1923|GFD|
|||<br>12Tallow|Wholesaleprice|UScenta‘lb|Jan-1910|GFD|
||Grains|<br>13Barley|<br>No.2|<br>UScenta'lb|Jan-1894|GFD|
|||<br>14 Corn|<br>No. 2 yellow|<br>UESbushel|Jan-1860|GFD|
|||13 Flaxseed|Averageprice to farmers|USS/bushel|Jan-1901|GFD|
|||16 Oats||USS bushel|Jan-1826|GFD|
|||17 Rice|Bangkok|UsSTm|Oct-1914|GFD|
|||18 Wheat|HardRedWinter, No. 2,US|USS bushel|Jol-1841|GFD|
||Other|19 Butter||UScents‘pound|Jan 1890|GFD|
||food|20 Cheese|Cheese40-lb. Blocks|UScents‘pound|Jan-1929|GFD|
|||21 Eggs||UScents/‘douzen|Jan 1890|GFD|
|||22 Live Cattle||UScents/pound|Jan 1858|GFD|
|||23 LiveHog||UScents‘pound|Jan 1858|GFD|
|||24 Milk||Usscwr|Jan-1590|GFD|
|||23 Oranges||UsSsTm|Jan-1914|GFD|
|||26 Pepper<br>|Black pepper inNewYork<br>|UScents'lb<br>|Dec-1919<br>|GFD<br>|
|||27 Sheep|SheepAv. Price|UsSscwr|Jan-1874|GFD|
|||28 Sugar|No. 11|UScenta'lb|Jan-1784|GFD|
|Raw<br>||29 Cotton<br>||UScenta‘lb<br>|Jan 1784<br>|GFD<br>|
|materials||30 Hides|Cattle hides|UScents‘pound|Jan-1890|GFD|
|||31 Lumber||U8S/1000 board feet|Jan-1891|GFD|
|||32 Rubber||UScentsth|Jan-1890|GFD|
|||33 Wool|64s, staple 2 3/4andup, US|UScents‘lh|Jan-1590|GFD|
|Metals<br>||34 Aluminum<br>|High grade, LME, cash<br>|Not specified<br>|Jan-1910<br>|GFD<br>|
|and<br>||35 Copper<br>|Highgrade|UScents‘lb<br>|Jan-1927<br>|GFD<br>|
|minerals||36 Ferromanganese||USS/zross ton|Jan-1908|GFD|
|||37 Gold|Goldbullion, NewYork|USS/ounce|Jan-1500|GFD|
|||38 Lead|Leadbar|USss'Tm|Jan 1800|GFD|
|||39 Mercury||UScenta'lb|Jan-1915|GFD|
|||40 Platinum||USS/ounee|Jan-1910|GFD|
|||41 Silver|99.9%Ag NewYork|U8cents/‘ounes|Jan 1784|GFD|
|||42 Steel scrap|Heavy melting steel scrap inChicago|Us}Tm|Jan-1894|GFD|
|||43Tin|Straits,pigs|UScentalb|Jan-1561|GFD|
|||<br>44 Wirebar|<br>CopperWirebarNewYorkdealer|<br>UScents/Lb|Jan 1800|GFD|
|||45Zine||UssTm|Jan-1875|GFD|
|Indexes||<br>1Ecomomist||a|Now1850|GFD|
|||<br>2 Food||-|<br>Dec-1910|GFD|
|||3 Metal||-|Dec-1910|GFD|
|||4Moody's||-|Jan-1928|GFD|
|||<br>3NonFood||-|Der-1910|GFD|
of a GARCH process to characterize our data. GARCH models, which have become extremely popular since their introduction by Engle (1982), allow for time varying volatility and permit the inclusion of additional structural determinants that can tell you how volatility is changing and what drives it.

We formally tested the validity of this approach by fitting an AR(1) model and found the coefficient to be statistical significant at 1% level for all commodities (see results for selected commodities in Table 2). We then tested the presence of heteroskedaticity using a Breusch-Pagan ARCH Test on the residuals of the AR(1) regression and we found evidence of heteroskedasticity for all commodities as shown in the right hand side of Table 2. Visual inspection of the residuals from AR(1) regressions clearly exhibit volatility clusters as shown in Chart 1 for selected commodities. Overall, the choice of a (G)ARCH process to model the behavior of commodity prices appears robust.

**Table 2. AR(1) coefficients and Breusch-Pagan ARCH Test for selected commodities**

||AR|(1)|<br>Breusch - Paga|n ARCH Test|
|---|---|---|---|---|
||Coefficient|t-Statistics|F - Statistics|Probability|
|Coal|0.99|221.2|179.7|0.00|
|Coffee|0.99|283.1|32.4|0.00|
|Copper|0.99|229.4|176.8|0.00|
|Corn|0.99|336.2|59.0|0.00|
|Cotton|0.99|340.9|119.3|0.00|
|Crude Petroleum|0.93|156.5|87.5|0.00|
|Gold|1.00|743.7|92.4|0.00|
|Lead|0.99|384.6|250.9|0.00|
|Rice|0.99|245.7|232.0|0.00|
|Silver|0.98|264.8|145.3|0.00|
|Sugar|0.98|286.7|453.8|0.00|
|Tea|1.00|243.3|144.7|0.00|
|Wheat|0.99|326.7|149.1|0.00|
|Zinc|0.99|372.9|378.0|0.00|

9
## **Chart 1. Residuals from AR(1) model on selected commodity prices**

_Actual minus fitted values_

## **_Copper Corn_**

<!-- Start of picture text --> 100 1.5<br>80<br>60 1<br>40<br>0.5<br>20<br>0<br>0<br>‐20<br>‐40<br>‐0.5<br>‐60<br>‐80 ‐1<br>‐100<br>‐120 ‐1.5<br><!-- End of picture text -->

## **_Sugar_**

## **_Wheat_**

<!-- Start of picture text --> 20 2.5<br>2<br>15<br>1.5<br>10<br>1<br>5 0.5<br>0 0<br>‐0.5<br>‐5<br>‐1<br>‐10<br>‐1.5<br>‐15 ‐2<br><!-- End of picture text --> _Source: Authors’ calculations_

# **4. Methodology**

Our search for an econometric methodology to detect breaks in commodity price volatility was based largely on three criteria. First, it ought to allow for the detection of multiple breaks. Second, the dates of the breaks should not be the result of an arbitrarily imposed choice but should instead be endogenously generated by the chosen methodology. Finally, given that commodity prices can be characterized as GARCH processes, methodologies specifically designed for ARCH-type of models would be preferred. On the basis of these three criteria we selected two tests: the Kokoszka and Leipus (KL 2000) test and the Inclan and Tiao (IT 1994) test. Both tests have been 10
applied in the literature to (G)ARCH-type models – see for example Hillebrand and Schnabl (2006) and Hillebrand (2005) for the use of the KL test and Granger and Hyung (1999) who applied the IT test to examine breaks in the absolute returns of the S&P 500.

To explain the KL (2000) test it is useful to start from the basic GARCH definition. ARCH models are generally defined by two equations: Where  _k_ are iid errors, and _a_ and _b_ ( _j_ ) are non-negative constants. These equations are suitable for series<sup>_r_</sup> _k_<sup>such that the observations are uncorrelated but exhibit clusters of</sup> volatility. Note that if  _k_ have zero mean, unit variance and the sequence <sup>_r_</sup> _k_ is weakly stationary, then: The KL test assumes that the parameters _a_ and _b_ ( _j_ ) change at an _unknown_ point _k_ * in such a way that the variance given by (2) changes. The test statistic is a CUSUM-type estimator _k_ ^ of _k_ * defined as follows: Where The normalized test sup  _R k_ ( _k_ )  /  ^ is asymptotically distributed as a Kolmogorov^ Smirnov process, where  is an estimate of the long-run standard deviation estimated using a VAR HAC estimator.<sup>10</sup> The general approach is to begin with the full set of observations to determine the first break. This break is then used to split the sample into two sub-series. The estimator then calculates breaks for the sub-series in order to

> 10 See den Haan and Levin (1997). For the choice of lags, we have followed the formula Lags = _floor_ (4(T(/100)^(2/9))).

11
establish additional breaks. This iterative procedure is stopped once a break is found to be statistically insignificant.

The IT test is based on a centered version of the cumulative sum of squares presented by Brown, Durbin, and Evans (1975). It is an algorithm that applies in principle to independent series and is designed to find a break in the (unconditional) variance with unknown location.

Define _Ck_ , the cumulative sum of squares of a series of uncorrelated random variables 2 {<sup>_a_</sup> _t_ } with mean 0 and variances  _t_ , _t_  2,1,..., _T_ .<sup>as follows:</sup> Also define _Dk_ , _k_  1,..., _T_ , with _D_ 0  _DT_  0 , as the centered cumulative sum of squares.

Time series with no breaks in variance would exhibit a plot of _Dk_ oscillating around 0. A sudden change in variance would cause the plot of _Dk_ to exhibit a pattern going out of the critical boundaries with high probability. Under variance homogeneity, the normalized statistic _T_ / 2 _Dk_ behaves asymptotically like a Brownian bridge. The advantage of the KL test is its validity under a wide class of processes, including long memory, GARCH-type and non-linear time series models. The relative advantage of the IT test is its simplicity and its independence from estimated long-run variance (which makes the test robust to time period selection).

The Montecarlo simulations of Andreou and Ghysels (2002) suggest that the IT test has power and only minor size distortions when applied to strongly dependent data, though it is not as powerful as the KL (2000) test. It suffers from size distortions (above 10%) for all data generating processes (high and low volatility persistence) but appears to have good power in detecting even small changes in the GARCH coefficients or the error 12
process for large _T_ . The test is not seriously affected by outliers for large samples ( _T_ > 3000).

The KL test has good power only for large and non-monotonic changes in the GARCH parameters for any data generating processes for the absolute returns rather than the squared. The KL (2000) test shows good power for detecting changes in the variance of the error terms in the GARCH process and appears fully robust to outliers. Finally, as the sample size ( _T_ ) increases the performance of the test improves even for small change points.

We use both monthly and daily data on individual commodities in order to account fully for differences across commodity markets since both the mean and volatility in individual prices exhibits different break points. Additionally, the use of individual prices allows us to examine whether the relationship between prices of different commodities has changed over time. Further, a measure of how this relationship has changed permits an examination of the role of financial market integration in determining price dispersion or synchronization. Finally, we introduce robustness checks given the scale-dependence of measured volatility.

# **5. Results**

Both tests highlight the heterogeneity across individual commodities. Even in periods where volatility breaks are more common it is far from the case that all, or even most commodities, exhibit the same regime shifts. This can be illustrated by Chart 2 below, which shows the percentage of commodities in our sample for which we detect a break in any given decade. As Chart 2 highlights, in most decades the proportion of commodities that experience a break is relatively low (below 10-15 percent using the KL test and less than 50 percent using the IT test). Even in decades of very high volatility, like the 1910s, 1940s, and 1970s there is a number of commodity prices which did not exhibit breaks in volatility.

13
<!-- Start of picture text --> 80<br>B % of commoditieswith at least one break (IT)<br>60<br>40<br>o oa o oa o oa o o oa o oa o oa oa o o<br>Lo oOo TM oo a o ec TM om La uw io TM oo on o<br>oO oO| iss]Col oOqd oOad adnn qdnn nmad ond adm1 nmd edn edn nmd mna oaTM<br>@<br>=6<br>ry<br>o<br><!-- End of picture text -->

<!-- Start of picture text --> 25<br>@ % of commoditieswith at least one break (KL)<br>20<br>15<br>10<br>o o ao oO o o o oa o oO o o o oa o oOo<br>wo wo TM mo n o ct Ca om wT un wo TM oo oa o<br>oo oO oo Li] oO on nm nn on mn an n nm n n o<br>a<br>23<br>Fy<br>oo<br><!-- End of picture text -->
<!-- Start of picture text --> 40<br>30 @ BreaksUP<br>20 Breaks DOWN<br>‘ a<br>, —_ i ——— || |_| | | ||<br>-10<br>-20<br>-30<br>o oa o ao oa o o o ao oa o o oa ao o o<br>ira) wo ~ o on o od om om st wn wo TM oO an o<br>Oo oO oO ao oo n nn n an nn n nn nn n nn oa<br>ad ad ad ad ad ad qd ad ed ad ad ad ad ad ad Mm<br>2<br>Neoa<br>o<br><!-- End of picture text -->

<!-- Start of picture text --> 12<br>8 @ BreaksUP<br>Breaks DOWN a i a<br>-4<br>-8<br>o o o o oa o o a o o o o o oS o o<br>ay wo ~ a on o eq mTM om Ls wi wo TM~ oo a a<br>fol©@ fali] ce]od od@ a]a oda7 odan ad oda coala odn oda foala odn Coala amTM<br>Fa6@<br>oa<br><!-- End of picture text -->
<!-- Start of picture text --> 40<br>35 m@KL IT<br>ww<br>a<br>= 30<br>as]<br>6<br>— 25<br>E<br>G: 720<br>3<br>S15<br>= io<br>—<br>2<br>5<br>0 i<br>i) 1 2 3 4<br>Numberof Breaks<br><!-- End of picture text -->
<!-- Start of picture text --> 8<br>—— Breaks UP<br>6<br>Breaks DOWN<br>4<br>2 I<br>in) —_ ee ee<br>2<br>4<br>6<br>os es ee Ss es es ee eS ee a es es ad<br>nomaA nA nt mnt© nt nt ntti ntnannt mrmrinmninmemrimremrenonornamrrtrnt tt nt dA tt tnt nA tet tt tet nt ttrmatnt nt eArarmrararanrniartienraaraoanrnant tt eA tt tt tt tka tt nt nA tt a TnaosdNN<br><!-- End of picture text --> <!-- Start of picture text --> 2.0<br>—— Breaks UP<br>15<br>Breaks DOWN<br>1.0<br>O58<br>10<br>145<br>ARAN R AE NR NE NEN ENE NEN RNR NEN RENE NEN REN PONE ON<br>oom mm ow namnmMOmrmrenmreinmrmremrmoeramrrararrarararmraaaraeanrmrmnmarmarnaeranrnenranrneasd<br><!-- End of picture text -->
# **6. Conclusions**

Our paper is motivated by three main questions. First, is there a pattern of volatility across commodities over time? Second, is there a long-run trend in commodity price volatility? Third, are there identifiable breaks in commodity price volatility? For example, do we see changes in volatility when the world went from relatively open (1820 – 1913) to closed (1914 – 1949) and then to open (1950-2009)?

Drawing on a large unbalanced panel of monthly prices of 45 individual commodities and 5 commodity price indices we address these issues by implementing two tests for detecting structural change. Both tests have the advantage of not imposing a priori the dates of potential structural breaks. While both tests are based on CUSUM-type test statistics, they differ in how they establish the threshold above which a change in volatility is considered a structural break. The Kokoszka-Leipus test uses an estimate of the long-run variance of the entire time series to determine such a threshold level. As a result, it is a more stringent test resulting in fewer breaks and by and large only three periods in history are associated with breaks in volatility in most (but not all) commodities: the two world wars and the collapse of the Bretton-Woods system. The Inclan-Tiao (IT) test, in contrast, considers only the properties of the time series since the last identified break in volatility. As a result, threshold volatilities are re-defined every time a break is found. This results in less stringent thresholds and therefore more breaks in volatility – both upwards and downwards. Therefore, even though break-points may overlap, the IT test, constructed to be more sensitive, picks up more frequent shifts. However, the historical breaks coincide under both methodologies.

The main conclusions are as follows. First, the timing and number of breaks in volatility vary considerably across individual commodities. This result cautions against broad generalizations and the use of commodity price indices to analyze changes in volatility. Second, the three most significant breaks common to most (but not all) commodities, are the two world wars and the collapse of the Bretton-Woods system. In recent years, however, there has been an uptick in price volatility in a number of commodities. During the last food crisis though, it is clear that volatility spiked, starting to rise before the actual increase in price levels especially for the most tradable commodities. However, the 18
evidence suggests that structural breaks marking increased price volatility are subsequently followed by downward breaks in volatility so that there is no upward or downward trend in volatility over time.

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