Miguel Robles, Maximo Torero, and Joachim von Braun

INTERNATIONAL FOOD

POLICY RESEARCH INSTITUTE

sustainable solutions for ending hunger and poverty

Supported by the CGIAR

When Speculation

matter

IFPRI Issue Brief 57 • February 2009
2

These reactions began as consequences, not causes, of the 

price crisis, but they exacerbated the crisis and increased 

the risks posed by high prices. By creating a positive 

feedback loop with high food prices, they took on a life of 

their own, increasing price levels and price volatility even 

more, with adverse consequences for the poor and for 

long-term incentives for agricultural production. Because 

they impeded the free flow of food to where it is most 

needed and the free flow of price signals to farmers, these 

market failures imposed enormous efficiency losses on the 

global food system, hitting the poorest countries hardest.

Changes in supply and demand fundamentals cannot 

fully explain the recent drastic increase in food prices. 

Rising expectations, speculation, hoarding, and hysteria 

also played a role in the increasing level and volatility of 

food prices. The flow of speculative capital from financial 

investors into agricultural commodity markets has been 

drastic, and the number of future traded contracts is 

increasing over time. From May 2007 to May 2008, the 

volume of globally traded grain futures and options rose 

significantly. 

Excessive speculation in the commodity futures 

market could, in principle, push up futures prices and—

through arbitrage opportunities—spot prices above 

levels justified by supply and demand fundamentals. The 

supposed impact of speculation is sometimes confused, 

however, with the impact of hedging, which reflects 

consumers’ genuine concerns about future fundamentals 

and desire to hedge against risks. 

This brief analyzes the role of financial speculation in 

the behavior of agricultural prices in recent years.

What is speculation?

Speculation is the assumption of the risk of loss in return 

for the uncertain possibility of a reward. It is ordinarily understood to mean the purchase of a good for later resale 

rather than for use, or the temporary sale of a good with 

the intention of later repurchase in the hope of profiting 

from an intervening price change. (A broader definition of 

speculation could even include hoarding by consumers in 

times of perceived market risk, but that definition is not 

used here.) Only if a particular position involves no risk 

can it be called, strictly speaking, an “investment.” 

Financial speculation involves the buying, holding, 

selling, and short-selling of stocks, bonds, commodities, 

or any valuable financial instrument to profit from 

fluctuations in its price as opposed to buying it for use or 

for dividend or interest income. Speculation is one of four 

market activities in financial markets, along with hedging, 

long- or short-term investing, and arbitrage.

In the context of food markets, speculators are 

relatively risk-tolerant individuals who are rewarded for 

accepting price risks from more risk-adverse hedgers. 

A risk-adverse trader who is or anticipates holding 

the commodity (such as a farmer with a crop of wheat 

The food price crisis of 2007–08 had several causes—rising demand for food,

the change in the food equation through biofuels, climate change, high oil 

prices—but there is substantial evidence that the crisis was made worse by 

the malfunctioning of world grain markets. Dozens of countries imposed 

restrictions on grain exports that resulted in significant price increases, 

given the thinness of markets for major cereals.  number of countries adopted retail

price controls, creating perverse incentives for producers. Speculative price spikes built 

up, and the gap between spot and futures prices widened, stimulating overregulation and 

trader policing in some countries and causing some commodity exchanges in Africa and

Asia to halt grain futures trading. Some food aid donors defaulted on food aid contracts.

The World Food Programme (WFP) had difficulty getting access to enough grain quick

for its humanitarian operations. Developing countries began urgently rebuilding their 

national stocks and reexamining the “merits” of self-sufficiency policies for food security. 
approaching harvest) may hedge by selling now, in a 

forward or “futures” market, for future delivery at a 

currently determined price. An individual who is or 

anticipates being short the commodity (such as a miller 

of wheat) may hedge by buying now for future delivery 

at such a known price. Speculators in the futures market 

may be on the long and short side of any single such 

transaction, but in the aggregate their commitments must 

offset any net imbalances in the long and short hedgers’ 

positions. (A short position is the sale of a borrowed 

commodity with the expectation that the asset will fall in 

value. A long position is the buying of a commodity with 

the expectation that the asset will rise in value.)

Data an Proxies fo

 Speculatio

This analysis of the role of financial speculation in the 

behavior of agricultural prices in recent years focuses 

on trading activities in agricultural commodity futures 

markets, drawing on information about trading activities 

in the Chicago Board of Trade (CBOT), a leading 

agricultural futures exchange. The analysis encompasses 

four major commodities: maize, wheat, soybeans, and 

rice. To capture the size of and change in speculative 

behavior in agricultural commodity markets, we analyze 

four indicators: (1) volume of futures contracts, (2) open 

interest in futures contracts, (3) the ratio of volume to 

open interest in futures contracts, and (4) positions in 

futures contracts by noncommercial traders.

Monthly volume of futures contracts. This indicator 

captures the total number of trades in commodity futures 

contracts in the CBOT on a monthly basis, aggregating 

contracts with different maturities. Typically, contracts with 

maturities of 24 months or less are traded. The data show 

that traded volumes of agricultural commodity futures 

have increased significantly in recent years (Figure 1). From 

2005 to 2006, the average monthly volume of futures 

for wheat and maize grew by more than 60 percent and 

those for rice by 40 percent. In 2007, traded volumes 

again rose significantly for all four commodities, especially 

soybeans, whose monthly average was 40 percent larger 

than in 2006. During the first five months of 2008, only the 

volumes for maize seem to have stabilized, whereas the 

volumes for rice and soybeans were still growing at very 

high rates—47 percent and 40 percent, respectively. One 

reason for this increase in volumes and the subsequent 

impact on prices in recent years may be more active 

participation in these markets by speculators, especially 

short-term speculators, who open and close positions in a 

relatively short period of time. 

3

Wheat Maize Soybeans Rough rice

0

600

500

400

300

200

100

0

500

450

400

350

300

250

200

150

100

50

Monthly traded volumes Monthly open interest

Source: Chicago Board of Trade (CBOT).

Note: The volume index is a 3-month moving average. 

Volume index 

(1st quarter 2002 = 100)

Open interest index

(1st quarter 2002 = 100)

Feb-02

Jun-02

Oct-02

Feb-03

Jun-03

Oct-03

Feb-04

Jun-04

Oct-04

Feb-05

Jun-05

Oct-05

Feb-06

Jun-06

Oct-06

Feb-07

Jun-07

Oct-07

Feb-08

Wheat Maize Soybeans Rough rice

Feb-02

Jun-02

Oct-02

Feb-03

Jun-03

Oct-03

Feb-04

Jun-04

Oct-04

Feb-05

Jun-05

Oct-05

Feb-06

Jun-06

Oct-06

Feb-07

Jun-07

Oct-07

Feb-08

Source: Chicago Board of Trade (CBOT).

Note: The open interest index is a 3-month moving average. 

Figure 1—Monthly volume of futures contracts and open interest in futures contracts,

 February 2002–February 2008
Monthly open interest in futures contracts. Open interest 

describes the total number of futures contracts for a given 

commodity that have not yet been offset by an opposite 

futures position or fulfilled by delivery of the commodity. 

Every time a trader takes a position in the futures market 

(either long or short), it immediately generates an open 

position until this trader takes the opposite position or 

the contract expires. Open interest has been growing over 

the past five years (Figure 1), but the average growth rates 

for each commodity vary over time. From 2005 to 2006, 

the average monthly open interest in futures for wheat 

and maize grew by about 75 percent and that for rice by 

more than 90 percent. In 2007, however, open interest 

in maize and wheat declined slightly, and open interest in 

rice grew moderately, at 21 percent. Soybeans, meanwhile, 

increased by 40 percent on average in 2007, grew at a rate 

below 10 percent in early 2008, and started declining in 

February 2008. Furthermore, wheat experienced further 

decline in early 2008, and maize grew at a rate of only 

3 percent. These data on open interest may reflect 

the entry of medium- and long-term speculators into 

commodity futures markets, which may have played a role 

in the recent food price crisis.

Ratio of volume to open interest in futures contracts. The 

ratio of volume to open interest captures speculative 

market activity under the assumption that the majority 

of speculators prefer to get in and out of the market in a 

short period of time, in contrast to futures traders who 

are not engaging in speculation. Hence a speculator 

taking opposite positions (buying and selling contracts) in 

the market within days or weeks will generate an increase 

in monthly registered volumes but little change in monthly 

open interest. Therefore, changes in this ratio would potentially capture changes in speculative activity. In fact, this 

ratio has grown little over the past few years (Figure 2). 

In 2006, for instance, the ratio was declining across all four 

commodities. In 2007, the results were mixed, with 31 percent growth in the ratio for wheat and 17 percent growth 

in that for maize, but declining ratios for soybeans and 

rice. In 2008, however, both soybean and rice ratios were 

increasing, at 27 percent and 19 percent respectively, as 

wheat ratios continued to grow at 19 percent and maize 

declined slightly. Comparing this recent growth with 2005 

and 2006, when ratios for at least three commodities were 

declining on average, suggests that this ratio is a potential 

instrument to capture speculative behavior.

Ratio of noncommercial positions to total positions in 

futures contracts. The U.S. Commodity Futures Trading 

Commission (CFTC) classifies all of a reportable 

trader’s futures positions as either “commercial” or 

“noncommercial.” (Reportable traders are those who 

hold positions in futures and options at or above specific 

reporting levels set by the CFTC. It is estimated that 

the aggregate of all traders’ positions reported accounts 

4

Apr-02

Oct-02

Wheat Maize Soybeans Rice

0

10

9

8

7

6

5

4

3

2

1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Ratio of volume to open interest Ratio of noncommercial long positions to total 

reportable long positions

Source: Chicago Board of Trade (CBOT). Source: U.S. Commodity Futures Trading Commission (CFTC).

Ratio

(monthly volume / monthly open interest)

Ratio

Feb-02

Jun-02

Oct-02

Feb-03

Jun-03

Oct-03

Feb-04

Jun-04

Oct-04

Feb-05

Jun-05

Oct-05

Feb-06

Jun-06

Oct-06

Feb-07

Jun-07

Oct-07

Feb-08

Wheat Maize Soybeans Rough rice

Jan-02

Jul-02

Apr-03

Oct-03

Jan-03

Jul-03

Apr-04

Oct-04

Jan-04

Jul-04

Apr-05

Oct-05

Jan-05

Jul-05

Apr-06

Oct-06

Jan-06

Jul-06

Apr-07

Oct-07

Jan-07

Jul-07

Apr-08

Jan-08

Figure 2—Ratio of volume to open interest in futures contracts and positions in futures contracts by

 noncommercial traders, 2002–08
for more than 70 percent of the total open interest in 

any given market.) Futures positions in a commodity are 

classified as commercial if a trader uses futures contracts 

in that commodity for hedging purposes as defined by the 

CFTC; otherwise, a position is classified as noncommercial. 

Hence, whereas commercial positions are held for 

hedging purposes, noncommercial positions in futures 

contracts mainly represent speculative activity in pursuit 

of financial profits. This brief uses the CFTC classification 

to study the importance of speculative activity relative 

to hedging activity in recent years, looking at the ratio of 

noncommercial positions to total positions, for long as 

well as for short positions. Data incorporate only total 

reportable positions because only reportable positions are 

classified as either commercial or noncommercial.

The ratio of long noncommercial positions to total 

long positions seems to have grown in recent years. For 

each of the years from 2006 to 2008, the ratio’s weekly 

average has grown in at least three of the four commodity markets. For maize this ratio averaged 0.29 in 2005 

and reached 0.49 in the first five months of 2008. Similarly, 

increases have been observed for wheat and soybeans. 

For rough rice, this ratio has been more erratic over time. 

Although the ratio increased during 2008 compared with 

2007, it is still lower than observed levels in past years. In 

the case of short positions, there is less evidence of an 

upward trend in the relative importance of speculative positions in recent years. On the contrary, it seems 

that commercial short positions have become 

relatively more important. Overall, increasing participation by commercial hedgers in the futures 

markets has been matched by increasing participation by speculative investors. This situation 

does not mean, however, that short positions by 

speculators have not affected prices. Ultimately, 

the volume of short positions held by speculators 

has strongly increased over time, as has the volume of short positions held by hedgers.

Index traders’ net positions. Since 2006, the 

CFTC has provided information on futures and 

options trading by a new category of traders in 

selected agricultural markets known as index 

traders.

These traders generally replicate a commodity index by establishing long futures positions 

in a mix of commodity markets and then rolling 

those positions forward from future to future 

using a fixed methodology. Hence, most of these 

traders hold long-only futures positions. This category includes noncommercial traders, such as 

managed and pension funds, as well as commercial traders. 

Information is available for positions on futures and options contracts for wheat, maize, and soybeans. In the case 

of wheat index traders, long positions account for around 

40 percent of total open interest, whereas in the cases of 

maize and soybeans this proportion is around 25 percent. 

As long as these index traders enter the agricultural commodities futures and options markets for reasons other 

than hedging against commodity-specific risks, their trading 

positions are used here as a proxy for speculative activity. 

In particular, we look at net positions (long minus short 

positions). Figure 3 shows an upward trend for soybeans 

and maize from January 2006 to mid-2008. 

Eviof deCausal nceEf

This study statistically tested whether speculative activity 

in the futures market can be identified as a source of 

increasing agricultural commodity prices in 2007–08. The 

results show that speculative activities might have been 

influential, but the evidence is far from conclusive. 

The analysis here tested to what extent the selected 

indicators for speculative activity can help forecast spot 

price movements, using the Granger causality test (see the 

Appendix for details on this methodology). This test seeks 

5

0

500

450

400

350

300

250

200

150

100

50

Source: U.S. Commodity Futures Trading Commission (CFTC).

Note: Net positions = long-short positions.

Number of (equivalent) futures contracts 

(thousands)

Jan-3-06

Mar-3-06

May-3-06

Jul-3-06

Sep-3-06

Nov-3-06

Jan-3-07

Mar-3-07

May-3-07

Jul-3-07

Sep-3-07

Nov-3-07

Jan-3-08

Mar-3-08

May-3-08

Wheat Maize Soybeans

Figure 3—Index traders’ net positions in futures and options,

 January 2006–May 200
6

to determine whether past movements in one variable can 

help explain current movements in another one; if so, the 

latter variable is said to be caused by the former one. This 

econometric technique was applied to each agricultural 

commodity. Using monthly spot prices, as reported by the 

Food and Agriculture Organization of the United Nations 

(FAO), we investigated whether any of the proxies for 

speculation used here can be identified as causing (technically, “Granger”-causing) the corresponding price change. 

(More specifically, in a time-series setting, we looked at the 

current log prices and ran a regression on past log prices 

and the lagged proxy of speculation. Then this model was 

compared with a restricted model, which removed the 

lagged proxy variable using an F-test. Whenever we found 

evidence of nonstationary series, for either prices or speculation indicators, we used first differences, provided these 

were stationary. For more information, see the Appendix.) 

The tests were conducted by taking 30-month periods beginning with the period January 2002–June 2004 and moving ahead one month at a time until the period November 

2005–May 2008 was reached. For each commodity and 

each different speculation indicator, 49 causality tests 

were conducted as the period of analysis moved ahead 

one month at a time. As the analysis reached more recent 

periods, when prices started to increase more rapidly, the 

tests were able to show any indication that speculation 

was pushing prices up. Because data on index traders’ net 

positions before 2006 were unavailable, this rolling period 

strategy could not be used to analyze that indicator. In this 

case a simple causality test for the available period 

(2006–08) was conducted.

Table 1 summarizes the results of the causality tests. 

As shown, the size of trading activity in futures contracts 

when measured by volume or open interest separately 

shows no evidence of affecting commodity prices. The ratio 

of monthly volume to open interest in futures contracts, 

however, has an influence in forecasting price movements 

for wheat and rice. In other words, past changes in this 

ratio help to forecast future changes in the price of wheat 

and rice. In addition, for the case of rice the ratio of noncommercial long positions to total long reportable positions has an effect on prices. An analysis of the same ratio 

Indicator of speculation activity Wheat  Maize Soybeans

1. Monthly volume of futures contracts,

CB

2. Monthly open interest of futures

contracts, CB

3. Ratio of volume to open interest

(1)/(2) (futures contracts)

+ 

(Apr. 2005

Oct. 2007

+ 

(Dec 2004–

Jun. 2007)

4. Ratio of noncommercial positions to

total reportable positions (long)

+

(Apr. 2004–Oct

2006 and Sept. 

2005–Mar. 2008 

5. Ratio of noncommercial positions to

total reportable positions (short) 

+ (Mar. 2004

Sept. 2006 

and Jan. 2005–

Jul. 2007

+

(Aug. 2005

Feb. 2008)

6. Index traders’ net positions (long –

short positions)a

+

(Jan. 2006–

May 2008

n.a.

 

Source: Authors.

Note: “+” indicates evidence of causality. The starting period of the evidence of causality is in parentheses. “n.a.” indicates not available. aThis indicator combines futures and options positions using data available since January 20

Commodi

Table 1—Evidence of speculation activity affecting commodity price
7

for short positions provides additional evidence that 

speculation affects prices, with significant results in 

the soybean market. In the case of maize there are 

signs of causality for the ratio of noncommercial 

short positions to total short positions between 

March 2004 and September 2006 and during the 

30-month span lasting from January 2005 until July 

2007. Finally, a test of the influence of the net positions of index traders on commodity prices from 

January 2006 to May 2008 reveals positive evidence 

in the case of maize (a 95 percent confidence level 

is used to claim statistical evidence). 

Figure 4 provides a more detailed picture of 

cases in which evidence shows that speculation 

activity causes price changes. Typically, a Granger 

causality test produces an indicator, called an F statistic, that must be compared with another number 

called an F critical value. A positive difference indicates causality, and the bigger this difference, the 

more statistically significant the evidence. 

Conclusio

This analysis statistically tested whether speculative 

activity in the futures market can be identified as a 

source of the increasing agricultural commodity prices in 

2007–08. The results show that speculative activities might 

have been influential. The analysis also tested the extent 

to which selected indicators for speculative activity can 

help forecast spot price movements, producing evidence 

that some speculation indicators affect current commodity 

prices of wheat, rice, maize, and soybeans.

The excess price surges caused by speculation and 

possible hoarding could have severe effects on confidence 

in global grain markets, thereby hampering the market’s 

performance in responding to fundamental changes in supply, demand, and costs of production. More important, they 

could result in unreasonable or unwanted price fluctuations that can harm the poor and result in long-term, irreversible nutritional damage, especially among children.

Appropriate global institutional arrangements for preventing these market failures are missing. A global solution 

that prevents excessive speculation in food markets may 

be costly, but given the losses created by food price crises like the one in 2007–08, it will still have large positive 

net returns. It is clear that the incentives for speculation 

in food commodities could be reduced by (1) changing 

regulatory frameworks to limit the volume of speculation 

versus hedging, (2) making delivery on contracts or portions of contracts compulsory, (3) imposing capital deposit 

requirements when each futures transaction is made, or all 

three. These regulatory measures could be implemented 

case by case or as a platform through an international 

“alliance of commodity exchanges.” Difficulties could arise, 

however, in walking a line between ineffective regulators 

(like the U.S. Commodity Futures Trading Commission) 

and overzealous ones (like those in China and India). 

Market regulation also raises political economy concerns, 

including the possibilities that regulatory measures could 

benefit relatively small groups, that certain groups may 

capture control of the regulatory agency, that regulatory 

agreements may not be completed, and that countries may 

lack the institutional capacity to implement and enforce 

the regulatory measures. 

A new global institutional arrangement encompassing 

a “virtual reserve” could be an alternative solution (see 

the IFPRI policy brief Implementing Physical and Virtual 

Food Reserves to Protect the Poor and Prevent Market Failure, 

by Joachim von Braun and Maximo Torero. Washington, 

DC: International Food Policy Research Institute, 2009). 

This virtual reserve would consist of a coordinated 

commitment by member countries (the Group of 

Eight Plus Five plus some other major grain-exporting 

countries such as Argentina, Thailand, and Vietnam). Each 

country would commit to supplying funds, if needed, for 

intervention in the futures market. The innovative concept 

8

6

4

2

0

-2

-4

-6

Note: Positive numbers on vertical axis show evidence of influence. Index = F statistic - F critical value

Wheat: Volume/open interest

Rice: Volume/open interest

Rice: Ratio of noncommercial long positions

Maize: Ratio of noncommercial short positions

Soybeans: Ratio of noncommercial short positions Jan-06 Mar-06 May-06 Jul-06 Sep-06 Nov-06 Jan-07 Mar-07 May-07 Jul-07 Sep-07

Nov-07

Jan-08

Mar-08

May-08

Jul-04

Sep-04

Nov-04

Jan-05

Mar-05

May-05

Jul-05

Sep-05

Nov-05

Last month of a 30-month period

Figure 4—Evidence of speculation influencing commodity

 prices, July 2004–May 200
INTENATIONAL FOOD PO

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Copyright © 2009 International Food Policy Research Institute. All rights reserved. Sections of this document may be reproduced without the express permission of but 

with acknowledgment to IFPRI. Contact ifpri-copyright@cgiar.org for permission to reprint.

Miguel Robles (m.robles@cgiar.org) is a postdoctoral fellow in and Maximo Torero (m.torero@cgiar.org) is director of the Markets, Trade, 

Institutions Division (MTID) of the International Food Policy Research Institute (IFPRI). Joachim von Braun (j.vonbraun@cgiar.org) is director 

general of IFPRI.

FINANCIA

IFPRI’s research, capacity strengthening, and communications work is made possible by its financial contributors and partners. IFPRI receives its principal funding from 

governments, private foundations, and international and regional organizations, most of which are members of the Consultative Group on International Agricultural 

Research (CGIAR). IFPRI gratefully acknowledges the generous unrestricted funding from Australia, Canada, China, Finland, France, Germany, India, Ireland, Italy, Japan, 

Netherlands, Norway, South Africa, Sweden, Switzerland, United Kingdom, United States, and World Bank.

behind the virtual reserve is the signal that it would give 

to markets, including speculators. Although its presence 

alone would likely divert speculators from entering this 

market, the virtual reserve must be ready to trade grain 

when necessary. This concept could provide the kind of 

global collective action that is needed to facilitate wellfunctioning grain markets and to reduce the harm that can 

result from excessive price spikes.

This appendix explains the details behind the rolling regressions 

Granger causality tests. First, we selected the international price 

of a specific commodity      . The 

log of this price at time  was denoted as 



. Second, we focused 

on a speculation proxy variable. For each commodity there were 

five speculation proxies, denoted here as , where  

 and

 = noncommercial long ratio for commodity 

 = noncommercial short ratio for commodity 

 = volume-to-open interest ratio for commodity 

 = volume traded on short or long futures for commodity 

 = open interest for commodity 

All of these proxies refer to transactions in futures markets; data 

are taken from transactions in the Chicago Board of Trade. All 

variables are in a monthly frequency. A speculation proxy for a 

given time  was denoted as . The order of integration for 

each speculation proxy was tested. In the case of  and 

, the condition that the time series behave as stationary 

was imposed. We claim that this is by construction because these 

ratios are bounded between zero and one. If a given speculation 

proxy is integrated of order one, we then worked using its first 

difference. None of our proxies behave as integrated of order 

two or greater. Here, for exposition purposes, we assumed that 

all proxies behave as integrated of order one, and hence we used 

the first difference .

Third, we fixed a sample period of 30 months, starting in January 

2002. Then for every commodity price 



 and every speculation 

proxy for that commodity , we ran a one-way Granger 

causality test to examine whether the speculation proxy caused, 

in the Granger sense, the commodity price. As stated in the 

literature, by “Granger sense” we mean whether the speculation 

proxy helps forecast the commodity price. Then we rolled the 

30-sample period one month ahead and repeated the same 

Granger causality test exercise. The second exercise was thus a 

30-month sample starting in February 2002. We kept rolling the 

30-month sample ahead until we exhausted the available data. 

Each Granger causality test consisted of the following steps. First, 

we ran the following unrestricted model:











Notice that we incorporated only one speculation proxy in 

this unrestricted model, and we did exactly the same for each 

speculation proxy. One could incorporate more than one proxy 

or add other exogenous variables into this model. We chose not 

to do so because we wanted to keep the simplest unrestricted 

model (a pure autoregressive process) and study the forecasting 

ability of every speculation proxy against this simple model. 

To determine the lag structure, a general-to-specific approach 

was used, where more lags were considered in an original 

unrestricted regression than were thought to be necessary. Then 

we used the Bayesian-Schwartz criterion to define the most 

appropriate lag structure  for the specific commodity and 

speculation proxy combination. Once the unrestricted model 

was computed, we saved the residual sum of squares . 

Second, we ran the following restricted model:







Based on this restricted model, we computed the residual sum of 

squares . Finally, we constructed the following F-test:

  



 

  



where the null hypotheses is that 

 does not Granger-cause 

.

Appendix: Rolling Regressions Granger Causality











