Monetary factors of commodity prices using fuzzy binomial approach

Abstract

This paper relates the illustration of policy related to monetary announcement on various international commodity price and explore the similarities and differences of the effect in QE1, QE2, QE3, exit stage and interest hike stage through event study method and the whole sample VAR model and rolling sample VAR model. Results show that: (1) the implementation of unconventional monetary policy has a significant positive effect on the international commodity market, while the exit plan and the interest rate increase policy have some negative effects on the commodity markets, but the effects are not significant. (2) In terms of the VAR whole samples, it can be seen that unconventional policies of monetary simulated by reserve of federal have an importance in impact on international commodity prices. This paper developed a approach of fuzzy binomial that can be utilized in various projects using commodity prices using uncertainty. In terms of the analysis of the rolling samples, the cumulative effect on commodity prices during QE1 and QE2 are stronger than that of QE3, exit stage and interest rate hike stage in general.

Keywords

Monetary policy commodity price event study VAR model fuzzy binomial

1 Introduction

Since the demonstration of redefined and opening up strategies, China’s economy has grown rapidly and China has become a major manufacturing country, with an increasing demand for raw materials and other bulk commodities tied to the manufacturing process. With the sustained growth of bulk commodity demand, China will inevitably bear the pressure of international commodity price fluctuations across an extended time frame. In the wake of the financial crisis, the world’s major economies seemed coordinated in adopting various unconventional monetary policy measures, and commodities pricing experienced a V-shaped rebound from a sharp fall to a sharp rise. In April 2011, the CRB index, representing changes in international commodity prices, reached a record high of 579.68, about three times that of 2000. Since then, the commodity market has continued to cool down. By the end of 2018, the CRB index basically maintained a fluctuation at around 412.53, but the price was still much higher than levels at the beginning of the new century.

Some researcheres have analyzed the impact of supply and demand factors on commodity prices. Breitenfellner et al. [4] found that supply and demand were two important driving forces that could not be ignored in the process of studying the influencing factors of crude oil price. Bastourre et al. [9] adopted a smooth transition auto regression model to demonstrate that global demand for bulk commodities is a long-term determinant of price levels. Gilbert [8] found that when the ratio of inventory to sales of a bulk commodity is relatively low, the prices of bulk commodities will fluctuate dramatically if there is a significant decline in supply and a serious excess of demand. Aastveit et al. [24] constructed the FAVAR model and found that effects of real economic demand factors on crude oil price to be higher than other price factors. Arbatli and Vasishtha [12] found that the real demand generated by the rapid growth of emerging economies further pushes up the international commodity prices. Kilian and Hicks [25] compared the impact of the world’s major economies on the price of crude oil by using the predictive correction model, and proved that the rapidly developing emerging economies represented by the Asia-Pacific region were an important driving force for the rise in the price of crude oil from 2003 to 2008.

However, in the context of a global flood of liquidity, it is widely argued that the main driving force of the strength of bulk commodities is not “commodity attributes” under the influence of supply and demand, but “financial attributes” under the influence of monetary factors. At present, many scholars have studied the fact of factors related to monetary on prices of commodity. Akram [30] constructed a SVAR model with the samples data from 1990 to 2007 to confirm that the real rate of decline and the dollar’s weakness could lead to the rise of commodity prices, and the monetary authorities will take easing monetary policy to stimulate demand for commodities. Based on the background of global inflation and excess liquidity, Belke et al. [2] used OECD countries’ data from 1970 to 2008 as research samples, and empirically tested relations among currency, interest rates, and prices of final commodity and bulk commodity using integration VAR model. The results showed that money supply (global liquidity) was the key to determining long-term homogeneity of price trends for bulk commodity and final commodity. As a consequence, the deviation of bulk commodity prices from long-term equilibrium leads to the rise of consumer prices, and such transmission from bulk commodity prices to consumer prices is a monetary phenomenon. Browne and Cronin [14] analyzed the long-term dynamic equilibrium relationship among currencies, commodity prices and consumer prices with the co-integration VAR model, and found that currency shock would lead to excess adjustment of commodity prices, but not excess adjustment of consumer prices. Glick and Leduc [32] found that loose monetary policy statements would enhance the uncertainty of the market, make market participants adjust their economic growth expectations downward, and then lead to the continuous decline of commodity prices. Anzuini et al. [1] adopted a VAR model to empirically test the impact of the Federal Reserve’s loose monetary policy on bulk commodity prices. The results showed that monetary policy shocks had a significant but modest impact on overall commodity price indicators and sub-indicators. Byrne et al. [21] employed a FAVAR model to empirically test that the relationship between commodity prices and real interest rates is negative, and loose monetary policy will lead to the rise of commodity prices. Zhang [33] stated the equilibrium of long term relationship and asymmetric threshold integration relationship between common components of 20 types of international commodity prices and global liquidity expansion through adopting the threshold integration method. Huchet and Fam [27] adopted a EGARCH model to demonstrate that compared with the U.S. currency or financial indicators, the speculation in the futures market had a greater impact on the commodity prices. Zhang and Fan [6] constructed a SVAR model with the indexes of oil production, total demand, oil price, global liquidity and China liquidity from April 2003 to June 2013 to confirm that China’s monetary policy has an increasingly obvious impact on oil prices.

Existing research has provided a solid theoretical support for our in-depth analysis of the impact of monetary policy on bulk commodity prices, but most of the literature focuses on the overall effect of the impact, ignoring stage factors. In view of this, the second part of this paper adopts a statistical descriptive method – every study model to test announcement monetary effect announcement policy on commodity price, and compares the immediate effect of monetary policy at different stages. The third part employs the VAR full sample and rolling sample analysis method to discover the similarities and differences of the impact of monetary of unconventional policy and the Fed’s interest rate increase policy on commodity prices in QE1, QE2, QE3, exit stage and interest hike stage.

Fuzzy logic considered to as a possibility for formulating the two capabilities of humans. One is the obtaining the converse from the capability, arriving at the imprecision of environment, incompleteness of details and the other one is to analyze a wide variety of mental and physical models without any instrumentations and computations. The features which considers the fuzzy logic is that in fuzzy logic all is or not allowed to be degree of matter [3 , 34]. In the theory of generalized of uncertainty, which is associated to information through the idea of granular structure- a concepts that significantly a vital role in interaction of human with real world.

2 Analysis of theeffect of policy related to fed’s monetary announcement on international commodity prices

This paper adopts event study, a descriptive statistics model to test the significance of policy related to Fed’s statement on the international commodity price. The component of study model by Dolly [20], and was first utilized to modify the specific impact as mergers and acquisitions, issuing additional stocks and macroeconomic policies on stock prices. In recent years, the study of event method has broadly utilized to estimate the effect of announcement of policy monetary due to its concise and clear logic.

Krishnamurthy and Vissing-Jorgensen [5] used the occasion study method to study the influence of the large-value asset purchase program deployed by Fed for period crisis on market interest rates. Neely [7] used the event study method to study the impact of unconventional monetary policies on the actual and nominal expected return on long-term US bonds. Zhao and Wu [26] utilized the study of event test the sensitivity of China’s agricultural futures market to the bearing of international good and bad news during the financial crisis. Ma and Sun [18], Liu et al. [16] and An et al. [17] also used the method to analyze the study to analyze the bearing of the Fed’s monetary policies.

2.1 Empirical methods

The first step is to determine the sample event. The sample events selected in this paper contain the Federal Open Market Committee (FOMC) meeting related to the Fed’s policy of unconventional monetary launch, exit and interest rate hike policy, and the public speech by the Fed’s chairman. The initial event is FOMC’s first to purchase $100 billion in institutional debt and $500 billion in mortgage-backed securities. The closing event is FOMC’s announcement on October 29, 2014 to terminate its asset purchase program in the month. The rate hike policy started on December 16, 2015. The deadline for the interest rate hike event selected in this paper is December 19, 2018. Events related to unconventional monetary policies may also include minutes of the FOMC meeting and other public presentations, which contain information on unconventional monetary policy announcements but are less informative and not direct sources of information, so they are excluded from the selection of sample events.

According to the above criteria, 31 sample events were finally obtained, 14 of which were launch events of unconventional monetary policies, 8 were exit events of unconventional monetary policies, and 9 interest rate hike events. The time between the two event announcement dates of November 25, 2008 and December 1, 2008 was very short, the window period coincided, and the two events were both launch events of the unconventional monetary policy, so they were combined into one event. During data processing, the dates from November 25 to December 1 were regarded as the announcement dates of the event, and the average value was taken for the return fluctuation in international commodity prices. The Table 1 below gives details of the sample events.

Table 1
Events related to the Fed’s monetary policy

Event Date Content

2008.11.25 For the first time, the Committee announced that it will purchase $100 billion of agency debt and $500 billion of agency MBS.

2008.12.01 Bernanke spoke in public and offered that the Fed could purchase a lot of medium and long-term Treasury securities.

2008.12.16 The Committee will expand its purchases of agency debt and MBS in light of economic conditions.

2009.01.28 The Committee will expand its purchases of agency debt and MBS in light of economic conditions and prepares to purchase longer-term Treasury securities.

2009.03.18 The Committee will enhance its agencies commodity to $200 billion and MBS to $1.25 trillion respectively. Meanwhile, it decided to purchase $300 billion of medium and long-term Treasury securities.

2010.08.10 The Committee plans to maintain its securities holdings level by reinvesting principal payments from its holdings of agency debt and MBS in longer-term Treasury securities, and will continue to extend its maturing Treasury securities holdings.

Launch events 2010.08.27 At the Jackson Hole annual meeting of global central banks, Bernanke hinted at further easing policy.

2010.09.21 The Committee will provide additional easing measures as required by the economic recovery and price stability.

2010.11.03 The Committee plans to purchase a further $600 billion of longer-term Treasury securities by the second quarter of 2011, that is, about $75 billion a month.

2011.08.26 At the annual meeting of global central banks, Bernanke said that the US economic recovery is far from expectations and the Fed will take further stimulus policies to help the recovery.

2011.09.21 The Committee decided toextend the average maturity of its securities holdings. That is, the operation twist starts.

2012.06.20 The Committee decided to extend operation twist until the last year.

2012.09.13 The Committee will purchase additional MBS at a rate of $40 billion a month.

2012.12.12 The Committee decided to purchase $45 billion of securities a month after operation twist ended.

2013.12.18 The Committee decided to reduce its monthly asset purchases. This marks the first step in QE’s exit.

2014.01.29 The Committee obvious to endure to reduce the monthly asset purchase scale.

2014.03.19 The Committee obvious to endure to reduce the monthly asset purchase scale.

2014.04.30 The Committee obvious to endure to reduce the monthly asset purchase scale.

Exit events 2014.06.18 The Committee obvious to endure to reduce the monthly asset purchase scale.

2014.07.30 The Committee obvious to endure to reduce the monthly asset purchase scale.

2014.09.17 The Committee obvious to endure to reduce the monthly asset purchase scale.

2014.10.29 The Committee decided to terminate its asset purchase program this month. This marks the formal exit from unconventional monetary policy.

2015.12.16 The Committee finds to range of target to 1/4 to 1/2 percent.

2016.12.14 The Committee decided finds to range of target funds rate to 1/2 to 3/4 percent

2017.03.15 The Committee decided finds to range of target funds rate to 3/4 to 1 percent.

Interest rate hike events 2017.06.14 The Committee decided finds to range of target funds rate to 1 to 1–1/4 percent.

2017.12.13 The Committee decided finds to range of target funds rate to 1–1/4 to 1–1/2 percent.

2018.03.21 The Committee decided finds to range of target funds rate to 1–1/2 to 1–3/4 percent.

2018.06.13 The Committee decided finds to range of target funds rate to 1–3/4 to 2 percent.

2018.09.26 The Committee decided finds to range of target funds rate to 2 to 2–1/4 percent.

2018.12.19 The Committee decided finds to range of target funds rate to 2–1/4 to 2–1/2 percent.

Event	Date	Content
	2008.11.25	For the first time, the Committee announced that it will purchase $100 billion of agency debt and $500 billion of agency MBS.
	2008.12.01	Bernanke spoke in public and offered that the Fed could purchase a lot of medium and long-term Treasury securities.
	2008.12.16	The Committee will expand its purchases of agency debt and MBS in light of economic conditions.
	2009.01.28	The Committee will expand its purchases of agency debt and MBS in light of economic conditions and prepares to purchase longer-term Treasury securities.
	2009.03.18	The Committee will enhance its agencies commodity to $200 billion and MBS to $1.25 trillion respectively. Meanwhile, it decided to purchase $300 billion of medium and long-term Treasury securities.
	2010.08.10	The Committee plans to maintain its securities holdings level by reinvesting principal payments from its holdings of agency debt and MBS in longer-term Treasury securities, and will continue to extend its maturing Treasury securities holdings.
Launch events	2010.08.27	At the Jackson Hole annual meeting of global central banks, Bernanke hinted at further easing policy.
	2010.09.21	The Committee will provide additional easing measures as required by the economic recovery and price stability.
	2010.11.03	The Committee plans to purchase a further $600 billion of longer-term Treasury securities by the second quarter of 2011, that is, about $75 billion a month.
	2011.08.26	At the annual meeting of global central banks, Bernanke said that the US economic recovery is far from expectations and the Fed will take further stimulus policies to help the recovery.
	2011.09.21	The Committee decided toextend the average maturity of its securities holdings. That is, the operation twist starts.
	2012.06.20	The Committee decided to extend operation twist until the last year.
	2012.09.13	The Committee will purchase additional MBS at a rate of $40 billion a month.
	2012.12.12	The Committee decided to purchase $45 billion of securities a month after operation twist ended.
	2013.12.18	The Committee decided to reduce its monthly asset purchases. This marks the first step in QE’s exit.
	2014.01.29	The Committee obvious to endure to reduce the monthly asset purchase scale.
	2014.03.19	The Committee obvious to endure to reduce the monthly asset purchase scale.
	2014.04.30	The Committee obvious to endure to reduce the monthly asset purchase scale.
Exit events	2014.06.18	The Committee obvious to endure to reduce the monthly asset purchase scale.
	2014.07.30	The Committee obvious to endure to reduce the monthly asset purchase scale.
	2014.09.17	The Committee obvious to endure to reduce the monthly asset purchase scale.
	2014.10.29	The Committee decided to terminate its asset purchase program this month. This marks the formal exit from unconventional monetary policy.
	2015.12.16	The Committee finds to range of target to 1/4 to 1/2 percent.
	2016.12.14	The Committee decided finds to range of target funds rate to 1/2 to 3/4 percent
	2017.03.15	The Committee decided finds to range of target funds rate to 3/4 to 1 percent.
Interest rate hike events	2017.06.14	The Committee decided finds to range of target funds rate to 1 to 1–1/4 percent.
	2017.12.13	The Committee decided finds to range of target funds rate to 1–1/4 to 1–1/2 percent.
	2018.03.21	The Committee decided finds to range of target funds rate to 1–1/2 to 1–3/4 percent.
	2018.06.13	The Committee decided finds to range of target funds rate to 1–3/4 to 2 percent.
	2018.09.26	The Committee decided finds to range of target funds rate to 2 to 2–1/4 percent.
	2018.12.19	The Committee decided finds to range of target funds rate to 2–1/4 to 2–1/2 percent.

The second step is to determine the event window and the estimation window. The event window refers to the time segment of the event impact. There is the possibility of information leakage or lagging reaction making the events impact of a cumulative effect. In the event study, n₁ days (t = –1, –2, –3,..., –n₁) before the announcement of the event (t = 0) and n₂ days (t = 1, 2, 3,..., n₂) after the announcement is generally selected as an event window.

The third step is to determine the estimation model of excess return. To estimate the excess return of international commodity prices during the event window, their normal cost of reappearance should be first projected. This paper adopts the ARMA model and uses the data in the estimated window to obtain the evolution law of the return fluctuation in commodity prices. An ARMA (p, q) process can be written as follows: $\begin{matrix} R_{t} = c + α_{1} R_{t - 1} + α_{2} R_{t - 2} + \dots + α_{p} R_{t - p} + ɛ_{t} \\ + θ_{1} ɛ_{t - 1} + θ_{2} ɛ_{t - 2} + \dots + θ_{q} ɛ_{t - q} \end{matrix}$ (1) where, R_t is the return rate of international commodity price in the t-th period; ɛ_t is the white noise process with a variance of σ²; c is a constant term; α_i and θ_j are autoregression coefficients and moving average coefficients, respectively.

This paper uses the RJ/CRB futures price index as an indicator of global commodity prices. The commodities covered by the index are bulk ones of raw material nature, and the prices come from the futures market, so the index can reflect the overall dynamics of global commodity prices in a timely manner and in a good way. The data comes from the WIND database. The return rate of international commodity price is equal to: $R_{t} = IN (\frac{{crb}_{t}}{{crb}_{t - 1}}) * 100$ (2)

After the ARMA model is obtained for each sample, heteroscedasticity tests are performed to observe whether the residual sequence has an ARCH effect. If there is an ARCH effect, the GARCH model is further used for estimation.

After the estimation model of the return cost is determined, the rate of return of the event window is predicted and ${\hat{R}}_{t}$ is obtained. The excess return is the difference between the actual rate of return and the normal rate of return predicted, namely: ${AR}_{t} = R_{t} - {\hat{R}}_{t}$ (3)

Further, in instruction to fully understand the influence of events, the scattered excess returns need to be aggregated along the time path. The cumulative excess return for event i under the event window is defined as: ${CAR}_{i} (t_{1}, t_{2}) = \sum_{t = t_{1}}^{t_{2}} {AR}_{it}$ (4)

Meanwhile, for all events of the same type, the average excess return for the t-th period and the average cumulative excess return for the period (t₁, t₂) are obtained, namely: $\bar{{AR}_{t}} = \frac{1}{N} \sum_{i = 1}^{N} {AR}_{it}$ (5) $\bar{CAR (t_{1}, t_{2})} = \frac{1}{N} \sum_{i = 1}^{N} {CAR}_{i} (t_{1}, t_{2})$ (6)

Where, N is the sample size, -5 ⩽ t₁ ⩽ t₂ ⩽ 5.

Finally, in order to determine whether the monetary policy announcement has a significant impact on international commodity prices, we need to make a significance test of excess returns. This paper adopts both the parameter test and the non-parametric test. The selection of the two different test methods is conducive to comparing the stability of the empirical results.

First, the parameter test method is introduced. The null hypothesis is established as H0: [t₁, t₂]. The average cumulative excess return $\bar{CAR (t_{1}, t_{2})}$ is zero. The following test statistic is constructed: $J = \frac{\bar{CAR (t_{1}, t_{2})}}{\sqrt{t_{2} - t_{1} + 1}} {(\frac{N (L - 2)}{L - 4})}^{1 / 2}$ (7)

It can be known that the test statistic order the common mean along with the distribution of 0 and 1 below the variance, where L is the length of the estimation window.

Secondly, this paper adopts the Wilcoxon signed rank test method in nonparametric test to make a significant test on the excess return. The Wilcoxon signed rank test is a widely used nonparametric test method. Its essence is to analyze whether the return of actual values in the event window are significantly different. The hypothesis test is H0: there is no variances amongst the term and the return normal. The main steps of the test method are as follows:

First, calculate the variances amongst the term and the return normal, which is the average excess return $\bar{{AR}_{t}}$ . Arrange the absolute values of the differences from large to small and give the rank R, starting from Rank 1 to Rank 11.

Second, divide R into a positive value portion R+ and a negative value portion R- to obtain sum of ranks: T⁺ = ∑R⁺, T^- = ∑R^-.

Third, construct the statistics. $Z = \frac{T - 0}{\sqrt{\frac{n (n + 1) (2 n + 1)}{6}}}$ (8)

It follows a common distribution with values of mean of 0 and 1 below the variance, where T = T⁺ - T^-, n = 11.

2.2 Empirical results

Table 2 lists the average excess returns ( $\bar{{AR}_{t}}$ ), average cumulative excess returns ( $\bar{CAR (t_{1}, t_{2})}$ ), and test statistic J of average cumulative excess returns generated from the impact of Fed’s launch of and exit from unconventional monetary policies on international commodity prices. It can be seen that in the entire event window, the average excess return brought by the launch event to the international commodity prices is mostly positive, and the fluctuation in the four days before the component announcement date (t = –4) is the largest, reaching0.7364. The average cumulative excess return from the launch event shows an upward trend over time, eventually reaching2.1057. The positive and the negative average excess returns caused by the exit event are not much different. On the first day after the event announcement date (t = 1), the fluctuation is the largest, reaching –0.4534, and the cumulative excess return for the entire event window is –0.1284. The average excess return from the interest rate hike event is mostly negative. The maximum fluctuation on the five days before the event announcement date (t = –5) is –0.5284, and the cumulative excess return for the entire event window is –1.2582. Moreover, according to the results of the parameter test, the launch event is statistically significant except for t = –5, while the exit event and the interest rate hike event are very low in significant level.

Table 2
Results of excess return and significance test

Event date Launch event Exit event Interest rate hike event

$\bar{{AR}_{t}}$ $\bar{CAR (t_{1}, t_{2})}$ J value $\bar{{AR}_{t}}$ $\bar{CAR (t_{1}, t_{2})}$ J value $\bar{{AR}_{t}}$ $\bar{CAR (t_{1}, t_{2})}$ J value

–5 0.0580 0.0580 0.2115 –0.1179 –0.1179 –0.3370 –0.5284 –0.5284 –1.6015

–4 0.7364 0.7944 2.0464^ 0.2039 0.0860 0.1737 0.0979 –0.4305 –0.9226

–3 0.2647 1.0591 2.2275^ –0.0850 0.0010 0.0016 –0.0701 –0.5006 –0.8760

–2 0.0160 1.0751 1.9583^* –0.1978 –0.1968 –0.2812 –0.1618 –0.6624 –1.0038

–1 0.6663 1.7414 2.8371^* 0.3078 0.1110 0.1419 –0.2499 –0.9123 –1.2366

0 0.0488 1.7902 2.6624^* 0.1366 0.2476 0.2889 –0.1491 –1.0614 –1.3134

1 0.0100 1.8002 2.4786^** –0.4534 –0.2058 –0.2223 –0.4007 –1.4620 –1.6749*

2 –0.2035 1.5967 2.0564^ –0.0767 –0.2825 –0.2855 0.1924 –1.2696 –1.3606

3 0.1684 1.7650 2.1433^ –0.1384 –0.4209 –0.4010 –0.1562 –1.4258 –1.4406

4 0.0090 1.7740 2.0436^ 0.0020 –0.4189 –0.3786 0.1313 –1.2945 –1.2408

5 0.3317 2.1057 2.3128^ 0.2905 –0.1284 –0.1107 0.0363 –1.2582 –1.1499

Event date	Launch event	Exit event	Interest rate hike event
–5	0.0580	0.0580	0.2115	–0.1179	–0.1179	–0.3370	–0.5284	–0.5284	–1.6015
–4	0.7364	0.7944	2.0464^**	0.2039	0.0860	0.1737	0.0979	–0.4305	–0.9226
–3	0.2647	1.0591	2.2275^**	–0.0850	0.0010	0.0016	–0.0701	–0.5006	–0.8760
–2	0.0160	1.0751	1.9583^*	–0.1978	–0.1968	–0.2812	–0.1618	–0.6624	–1.0038
–1	0.6663	1.7414	2.8371^***	0.3078	0.1110	0.1419	–0.2499	–0.9123	–1.2366
0	0.0488	1.7902	2.6624^***	0.1366	0.2476	0.2889	–0.1491	–1.0614	–1.3134
1	0.0100	1.8002	2.4786^**	–0.4534	–0.2058	–0.2223	–0.4007	–1.4620	–1.6749*
2	–0.2035	1.5967	2.0564^**	–0.0767	–0.2825	–0.2855	0.1924	–1.2696	–1.3606
3	0.1684	1.7650	2.1433^**	–0.1384	–0.4209	–0.4010	–0.1562	–1.4258	–1.4406
4	0.0090	1.7740	2.0436^**	0.0020	–0.4189	–0.3786	0.1313	–1.2945	–1.2408
5	0.3317	2.1057	2.3128^**	0.2905	–0.1284	–0.1107	0.0363	–1.2582	–1.1499

Note: ^***means statistically significant at the 1% level; ^**means statistically significant at the 5% level. ^*means statistically significant at the 10% level.

In order to supplement the parametric test, the follow lists the results of the Wilcoxon signed rank test for the monetary policy launch event, exit event and interest rate hike event. According to the Table 3 data, the Z statistic is 2.3117, which means that the events are statistically significant at the 5% level. Therefore, the original hypothesis is rejected, and the actual fluctuations are significantly different from the normal fluctuations. That is to launch policy significantly affects the international commodity prices.

Table 3

Results of Wilcoxon symbol rank test of launch event

n	Difference value	Absolute difference	Rank	Symbol rank
	$\bar{{AR}_{t}}$	$\| \bar{{AR}_{t}} \|$	R	–	+
1	0.0580	0.0580	5		5
2	0.7364	0.7364	11		11
3	0.2647	0.2647	8		8
4	0.0160	0.0160	3		3
5	0.6663	0.6663	10		10
6	0.0488	0.0488	4		4
7	0.0100	0.0100	2		2
8	–0.2035	0.2035	7	–7
9	0.1684	0.1684	6		6
10	0.0090	0.0090	1		1
11	0.3317	0.3317	9		9
Sum of symbol ranks: T^- = 7, T⁺ = 59				7	59

Table 4 lists the results of the Wilcoxon signed rank test for the exit event. The Z statistic is 0. This shows that the exit of the unconventional monetary policy has no significant impact on international commodity prices.

Table 4

Results of Wilcoxon symbol rank test of exit event

n	Difference value	Absolute difference	Rank	Symbol rank
	$\bar{{AR}_{t}}$	$\| \bar{{AR}_{t}} \|$	R	–	+
1	–0.1179	0.1179	4	–4
2	0.2039	0.2039	8		8
3	–0.0850	0.0850	3	–3
4	–0.1978	0.1978	7	–7
5	0.3078	0.3078	10		10
6	0.1366	0.1366	5		5
7	–0.4534	0.4534	11	–11
8	–0.0767	0.0767	2	–2
9	–0.1384	0.1384	6	–6
10	0.0020	0.0020	1		1
11	0.2905	0.2905	9		9
Sum of symbol ranks: T^- = 33, T⁺ = 33				33	33

Table 5 lists the results of the Wilcoxon signed rank test for the interest rate hike event. The Z statistic is –1.5115. This shows that the impact of the interest rate hike on international commodity prices is not significant.

Table 5

Results of Wilcoxon symbol rank test of interest rate hike

n	Difference value	Absolute difference	Rank	Symbol rank
	$\bar{{AR}_{t}}$	$\| \bar{{AR}_{t}} \|$	R	–	+
1	–0.5284	0.5284	11	–11
2	0.0979	0.0979	3		3
3	–0.0701	0.0701	2	–2
4	–0.1618	0.1618	7	–7
5	–0.2499	0.2499	9	–9
6	–0.1491	0.1491	5	–5
7	–0.4007	0.4007	10	–10
8	0.1924	0.1924	8		8
9	–0.1562	0.1562	6	–6
10	0.1313	0.1313	4		4
11	0.0363	0.0363	1		1
Sum of symbol ranks: T^- = 50, T⁺ = 16				50	16

3 Estimation of effects of dynamic monetary policy announcement on international commodity prices

The previous paper utilizes the event of study technique to analyze the effect of Fed’s unconventional monetary policy statement on international commodity prices, focusing on the analysis of the immediate effects of monetary policies. Next, we will use the VAR perfect to test the dynamic belongings of unconventional monetary policies and interest rate hike policies on international commodity prices based on full-sample and rolling samples respectively.

3.1 Model setting and data description

VAR model is a data-driven modeling method that is commonly applied to predict. It is characterized by directly forming the model by using every variable in model as component of the value ranges of every variables which are endogenous without significant definition of relationship amongst variables. Since all the variables contained in the model are regarded as endogenous variables, complex problems such as distinguishing between endogenous and exogenous variables and recognizing models are avoided, thus solving the endogenous problems that may exist in regression analysis-based study methods.

The lag of VAR model p-order without exogenous variables can be described as follows: $\begin{matrix} y_{t} = A_{1} y_{t - 1} + \dots + A_{P} y_{t - p} + u_{t} \\ t = 1, 2, \dots, T \end{matrix}$ (9) where y_t is a variable k-dimensional endogenous vector, A₁, ... ,A_p is the estimated k×k dimensional coefficient matrix, and T is the number of samples. u_t is a k-dimensional random perturbation vector whose elements in the same period can handle to every, but does not related to their hysteresis range, and does not related pertaining to variable on different side. The above formula can be expanded as follows: $\begin{matrix} [\begin{matrix} y_{1 t} \\ y_{2 t} \\ ⋮ \\ y_{kt} \end{matrix}] = A 1 [\begin{matrix} y_{1 t - 1} \\ y_{2 t - 1} \\ ⋮ \\ y_{kt - 1} \end{matrix}] + \dots + Ap [\begin{matrix} y_{1 t - p} \\ y_{2 t - p} \\ ⋮ \\ y_{kt - p} \end{matrix}] + [\begin{matrix} μ_{1 t} \\ μ_{2 t} \\ ⋮ \\ μ_{kt} \end{matrix}], \\ t = 1, 2, \dots, T \end{matrix}$ (10)

That is, the VAR(p) model containing k time series variables consists of k equations.

Based on the study purposes of this paper, we construct a four-variable VAR model that contains monetary policies, international commodity prices, output levels and price levels. The sample duration is from December 2006 to December 2018, and monthly data is selected. This paper uses the RJ/CRB pretends to index of prices as an indicator of level change in global commodity prices, and the data comes from the Wind database 1 . The term spread 2 is used as a proxy variable for monetary policies, the output level and price level are based on the US industrial production index and US consumer price index 3 , all three figures come from the fed’s economic database. 4

3.2 Empirical results

First of all, in order to ensure the stability of the empirical data, the unit root method test is needed to test the stability of the data. In this paper, the unit root test is performed using the Augmented Dickey-Fuller(ADF) method proposed by Dickey and Fuller [11]. Under the premise of determining whether the variable sequence unit root equation has an intercept term and a time trend, the ADF test is performed on the variable sequence, and the results are shown in Table 6. CRB, SP, IP, and CPI represent international commodity prices, term spreads, industrial output and price levels, respectively.

Table 6
Results of stability test

Variable I(c,t,k) ADFstatistics Critical values of t-statistic at different confidence levels Whether there is a unit root

0.01 0.05 0.10

CRB (0,0,2) –0.817200 –2.581349 –1.943090 –1.615220 I(1)

DCRB (0,0,1) –4.972306 –2.581349 –1.943090 –1.615220 I(0)

SP (c,0,1) –2.237443 –3.476472 –2.881685 –2.577591 I(1)

DSP (c,0,0) –9.536163 –3.476472 –2.881685 –2.577591 I(0)

IP (0,0,3) –0.143977 –2.581466 –1.943107 –1.615210 I(1)

DIP (0,0,3) –3.023236 –2.581584 –1.943123 –1.615200 I(0)

CPI (0,0,1) –0.040202 –2.581233 –1.943074 –1.615231 I(1)

DCPI (0,0,0) –7.056342 –2.581233 –1.943074 –1.615231 I(0)

Variable	I(c,t,k)	ADFstatistics	Critical values of t-statistic at different confidence levels	Whether there is a unit root
CRB	(0,0,2)	–0.817200	–2.581349	–1.943090	–1.615220	I(1)
DCRB	(0,0,1)	–4.972306	–2.581349	–1.943090	–1.615220	I(0)
SP	(c,0,1)	–2.237443	–3.476472	–2.881685	–2.577591	I(1)
DSP	(c,0,0)	–9.536163	–3.476472	–2.881685	–2.577591	I(0)
IP	(0,0,3)	–0.143977	–2.581466	–1.943107	–1.615210	I(1)
DIP	(0,0,3)	–3.023236	–2.581584	–1.943123	–1.615200	I(0)
CPI	(0,0,1)	–0.040202	–2.581233	–1.943074	–1.615231	I(1)
DCPI	(0,0,0)	–7.056342	–2.581233	–1.943074	–1.615231	I(0)

Note: (c,t,k) respectively represent the intercept, time trend and lag order in the equations tested; the lag order is determined according to the minimum value of AIC or SC; D denotes the first order difference; I(0) stands for the rejection of the original unit root hypothesis at a significance level of 5%.

It can be seen from Table 6 that in the case where the significance level is 5%, the unit root is present in the ADF test of the original sequence of each variable, and the first-order difference variable corresponding to all variables rejects the unit root hypothesis at the significance level of 5%. Therefore, the international commodity prices, spreads, industrial output values, and price indices in the model are I (1) sequences.

The VAR model is constructed based on the 4-variable differential sequence. According to the majority principle, the optimal lag period of the model is determined to be three phases. This paper uses the impulse response analysis method to examine the impact of monetary policies on international commodity prices. The response of impulse function depicts the dominance of variables in model related to VAR on various other variables. Specifically, it is characterized by the effect of adding a standard deviation to SP is shown in Fig. 1. The horizontal axis of the figure denotes the number of lag periods (unit: month), the vertical axis characterizes the change of the interpreted variable, the solid line characterizes the impulse reply function, and the dotted line represents two standard deviation bands.

Fig.1

Response function of Impulse of every variable to spread shock.

First, for one standard error shock from the term spread, the price level after reaching the lowest point. From the fourth period, it shows a small positive response, and the corresponding cumulative impulse response function converges to a positive value (0.000920) from the sixteenth period. This shows that changes in the term spread have a negative driving effect on price levels in the short term and little effect in the long term.

Second, for one standard error shock from the term spread, the international commodity price has a negative response, reaching a negative lowest point (–0.002726) in the second period, and then gradually rising, showing a positive effect in the third period and reaching a positive highest point (0.006766). The corresponding cumulative impulse response function converges to a small positive value (0.031805) from the fourteenth period, which reflects that the impact of the spread change on the commodity price is negative in the short term. Overall, the implementation of the bond purchase plan has a certain role in promoting commodity prices, but in the long run, the impact is small.

Third, for one standard error shock from the term spread, the industrial output first shows a positive response, then alternates between the positive and negative responses, and decays to zero in the twentieth period. The corresponding cumulative impulse response function converges to a positive value. This shows that the change in spreads has a small positive impact on industrial output.

It is necessary to further study the impact of industrial output and price levels on commodity prices. As can be seen from Fig. 2, for one standard error shock from the price level, the commodity price showed in the fourth period. After that it shows the trend of gradually decaying towards zero. From the perspective of the entire observation period, the impact of price levels on commodity prices is mainly positive, but it is not significant.

Fig.2

Impulse response function of CRB to CPI.

Figure 3 depicts the impulse response function of commodity prices to industrial output. For the shock from industrial output, commodity prices show a significant positive response, reaching a higher in the third duration, after which there is a tendency to zero in the twentieth period, indicating that changes in industrial output.

Fig.3

Impulse response function of CRB to IP.

The lively relationship amongst commodity prices and the Fed’s monetary policy can’t be clearly figured out through the whole sample study for the unconventional monetary policy of the Fed has not been implemented consistently both on the intensity and direction during three rounds of QE, exit process and interest rate increase 5 . In this paper, the analysis approach of circularly rolling samples by reference to research ideas of Zhu [10] is used to have at various stages. To be specific, the whole samples are drawn from December 2006 to December 2018, 48 months are selected as an inspection period in the model construction, 98 inspection periods are set for the whole samples, and the VAR model estimation is carried out for each inspection period. Fig. 4 shows the maximum response value and cumulative response value 6 of international commodity price against the shock of term spread in each inspection period. Each time point on the horizontal axis represents the inspection period of four years after that time. For example, 2006–12 represents the inspection period from December 2006 to November 2010.

Fig.4

Time-varying trend of CRB impact response to SP in rolling cycle VAR analysis.

The decline in the short-term amplitude of the response of international bulk commodity prices to term spread shocks can be observed from the sample 2006–12 7 . The maximum response amplitude of this sample reached 0.014208 and that of the sample 2007-02 reached 0.0011368, with the cumulative response value down from 0.054733 to 0.040791. That indicates compared to QE1, the QE2 further adopted in November 2010 produced a weakened impact on bulk commodity prices within a short term. Then, the maximum response value and cumulative response value immediately witnessed a slight rise. Both values of the sample 2007–09 reached the top during the test period, with the former being 0.020689 and the latter up to 0.091132. Just in August 2011, Ben Shalom Bernanke, when delivering a speech at the annual global meeting of central banks, indicated the further efforts of FRB in incentive policies in favor of economic recovery. It shows that the policy signal regarding the further formulation of economic incentive plans released at the meeting has significantly impacted bulk commodity prices.

Subsequently, both maximum response amplitude and cumulative response value saw a trend of decline until the sample 2009-10. During this period, the former decreased to 0.006956 and the latter to 0.005547. It demonstrates the operation twist introduced in September 2011 as well as the decision to extend this practice to the end of the year made in the late June 2012 weakened the term spread shock. It further indicates that the launch of QE3 in September 2012 produced fewer impacts on bulk community prices relative to QE1 and QE2.

For the samples 2009–10 to 2010-05, both values above witnessed a slight rise. The former rose to 0.011151 and the latter to 0.013019. That indicates that the decision by FOMC to reduce bond purchases in December 2013, which marked the first step of QE’s exit, contributed to the slight rise in the shocks against bulk commodity prices.

Through a slight rise, both values saw a new round of shock adjustments and an overall trend of decline. For the samples 2010-05 to 2011-09, the maximum response amplitude decreased to 0.006661 and cumulative response amplitude to 0.002809. It indicated the slightly weakened impact of several plans to cut bond purchases on bulk commodity prices since January 2014. Immediately, both values rebounded in a V shape till the former rose to 0.014988 and the latter to 0.034566 for the sample 2011-11. That reflects the enhanced impact of FOMC’s plan to terminate the asset purchase plan in October 2014 on term spread shocks.

Subsequently, both maximum response amplitude and cumulative response amplitude fluctuated stably. For the samples 2011-11 to 2013-02, the former was basically stable at around 0.018 and the latter fluctuated between 0.02 and 0.03. For samples 2013-02 to 2014-12, both values above witnessed a decline to certain degrees and fluctuated by 0 to 0.01. That shows the gradually weakened impact of term spread shocks following the introduction of a series of interest hike policies in December 2015.

Figure 5 shows the duration of the impact of term spread shocks on bulk commodity prices (sustained shock period curve) and the duration when the impact reaches the maximum (peak period curve). Specifically, the acting duration of term spread shocks started to increase since the sample 2007-3, fluctuated in periods 16 to 18 and witnessed a trend of decline following the sample 2010-1. It indicates that the adoption of the bond purchase plan enabled longer impacts of term spread shocks while the exit from the plan made the impact duration shorter. Since the sample 2012-1, the trend was maintained for 15 periods within a short term but was shifted to decline later and then fluctuated during the periods 9 to 13, showing further shortened duration of term spread shocks due to the adoption of interest hike policies relative to the previous QE policies. The peak period curve fluctuated in the periods 2 to 6 and then in periods 2 to 3 before the sample 2012-1, reflecting more rapid response of the interest hike policies introduced compared to a series of QE policies launched by FRB.

Fig.5

Sustained and peak shock period in VAR analysis during the rolling cycle.

Overall, the adoption of QE policies has caused significant positive shocks to bulk commodity prices, meaning the widened term spread would push the rise in bulk commodity prices. Additionally, the term spread shocks from the three rounds of quantitative easing at the end of each period produced a negative effect to some degrees (not marked in the chart), signifying that the continuous injection of liquidity would cause the decline in bulk commodity prices in turn. Seen from the maximum response value and cumulative effect, the positive shocks of QE1 and QE2 appears more significant than QE3 and interest hike policies. Also, the period QE saw a slower response to term spread shocks compared to that of interest hike period but a longer sustained shock duration relative to the interest hike cycle.

4 The binomial fuzzy model

In this model, a binomial fuzzy model is developed to estimate the commodity investment that enables association with real options. The ranges of the factor involving the prices of commodity which is estimated by valuation method. However, the components are evaluated by numbers using fuzzy when the extended is calculated; thus extended is known fuzzy binomial approach.

The valuation of the proposed model is based on the prices described for the commodity. Assuming there exist the option of call with the existing range of significant asset D₀ and prices S which is exercising, the ranges of the asset which is J_x probability to increase to xD₀ or J_d drop probability to dD₀ in certain period. The components x and d illustrate the jumping down and up component of the asset initial range, individual. A single time tree binomial asset which is underlying range are depicted in Fig. 6.

Fig.6

Underlying asset binomial tree for single period.

Z_{0} = \frac{1}{(1 + f)} [J_{d} Z_{ld} + J_{x} Z_{lx}]

(11)

Here in which f represents the rate of free interest, and J_x and J_d are considered as neutral risk probability, which are estimated by the given formula. $J_{d} = \frac{(1 + f) - x}{(d - x)}$ (12)

Therefore, the commodity price or the existing price of the option is the substituted simulation of the values of commodity prices with neutral risk assessment probabilities. Also, under the information pertaining their finalised model scenario. The nature of knowledge often pretends values of vague instead of random ranges. Theory of fuzzy which is goaled at uncertainty which is rationally caused by the imprecision and the form of vagueness has given a basis for manipulating certain knowledge. In the application of relevant field decision making in commodity prices exist the instances of employing fuzzy required using triangular member function to determine the indexes profitably.

In certain strategy or investment pertaining to the prices of commodity, information often leads to random values rather than vague. Therefore this methodology involves uncertainty possibility that the deploying the fuzzy numbers of statistical data to estimate the parameters.

5 Conclusion

In case of the results of the event study approach, the implementation of the market generally has strong expectations before the launch of QE1, QE2, QE3 and operation twist. However, the exit plan initiated by the Fed since December 18, 2013 and the interest rate increase policy since December 16, 2015 have some negative effects on the commodity markets, but the effects are not significant. International commodity markets are more sensitive to the implementation of monetary policy than to the exit of unconventional monetary policy and interest rate increase.

Seen from the full VAR samples, the unconventional monetary policies adopted by FRB have produced a significant impact on international bulk commodity prices. During the whole interval of the samples, the CRB index has made a fast negative response to term spread changes but meant a small-scale positive effect in the long run. According to the analysis of rolling samples, the non-conventional monetary policies differed in the impact on bulk commodity prices during the three rounds of QE, exit and interest hike cycle. It can be observed that the shocks against bulk commodity prices during the periods QE1 and QE2 are generally stronger than the periods of QE3 and interest hike; and the corresponding sustained shock period witnessed a slight increase during QE1 and QE2 and a steady decrease during QE3 and the interest hike cycle.

As China’s dependence on international commodities remains high, we should pay full attention to the impact of monetary policy on commodity prices, manage market expectations by means of prudent regulation, strengthen the rational adjustment of economic policies, indorse the sound and steady growth of domestic economic market, and prevent the negative impact of large fluctuations in commodity prices on China’s economic industry.

Footnotes

Here, RJ/CRB based on monthly year on year data. Wind database link: .

We make a difference between the daily data of the yield rate of 10-year government bonds and the yield rate of 3-month treasury bonds, and get the monthly data by monthly average.

US industrial production index and consumer price index based on monthly year on year data.

Fed’s economic database link: .

QE1 refers to the period from November 2018 to March 2010; QE2 refers to the period from November 2010 to June 2011; QE3 from September 2012 to October 2014 and the exit period from December 2013 to October 2014 (The QE periods cover a series of exit events).

Only the absolute values of the maximum response value and the cumulative response value are discussed here.

The corresponding test period lasts from December 2006 to November 2010 and the sample time points appearing later in this article corresponds to relevant test periods.

Acknowledgments

This work was supported by the Humanity and Social Science Youth foundation of Ministry of Education of China under grant number [16YJC790118].

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