Nonlinear price transmission and asynchronous price bubbles: empirical evidence from China’s agricultural futures and spot markets

Figures & data

Table 1. Summary statistics for daily price returns ($\mathrm{\Delta }{p}_t$).

	Corn price returns:			Soybeans price returns:
	Futures $\mathrm{\Delta }{p}_t^f$	Spot $\mathrm{\Delta }{p}_t^s$	t-test p-value	Futures $\mathrm{\Delta }{p}_t^f$	Spot $\mathrm{\Delta }{p}_t^s$	t-test p-value
Statistics
Mean*1000	0.0459	0.4973	0.8390	−0.4415	0.3106	0.7902
Median*1000	0.0000	2.5143	0.0930	1.0096	0.8855	0.0272
Maximum	0.3047	0.0363	—	0.2251	0.2798	—
Minimum	−0.2809	−0.1252	—	−0.1984	−0.3025	—
|Max-Min|	0.5856	0.1615	—	0.4235	0.5823	—
Std. Dev.	0.0446	0.0166	—	0.0427	0.0430	—
Skewness	−0.3157	−2.3565	—	−0.1518	−0.3143	—
Kurtosis	16.2430	14.5997	—	6.4541	20.5056	—
Jarque-Bera test statistics	3369.0308	2998.1710	—	230.4412	5868.3166	—
p-value of Jarque-Bera test	0.0000	0.0000	—	0.0000	0.0000	—
Number of obs.	460	460	—	460	460	—

Both the mean and median values are multiplied by 1000. Original price data without logarithmic transformation has been normalized into [0,1] before summary statistics.

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Figure 1. Corn: price bubble periods for the futures and spot prices.

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15. Original price data without logarithmic transformation has been normalized into [0,1].

Figure 2. Soybeans: price bubble periods for the futures and spot Prices³

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15. Original price data without logarithmic transformation has been normalized into [0,1].

Table 2. Comparing standard deviations of different cases.

Standard Deviation	Corn	Soybeans
In actual data	0.2009	0.1852
Assuming perfect staggering	0.1859	0.1686
Assuming perfect synchronization	0.3718	0.3371
Difference from perfect staggering	8.0689%	9.8516%

The synchronization level is measured by the standard deviations of the actual proportion of price changes for each commodity. For a certain timing point, the proportion of price changes will be (n/460), if n price series change their own values at this timing point. Therefore, if prices are perfectly staggered among different spot markets, the proportion of price changes in any period would be equal to the average proportion of price changes over time and the standard deviation should be close to zero. If prices were perfectly synchronized, the proportion of price series in any period would be either 0 or 1 and the standard deviation should be close to 0.5 (Loy & Weiss, 2002).

The standard deviations when ‘assuming perfect staggering’ or ‘perfect synchronization’ are calculated from the actual number of bubbles for each commodity. The degree of ‘Difference from perfect staggering’ Calculated as $({\sigma }_{\mathit{st}}-{\sigma }_d)/\left({\sigma }_{\mathit{st}}-{\sigma }_{\mathit{sy}}\right)\ast 100\mathrm{\%}$, where ${\sigma }_d$, ${\sigma }_{\mathit{st}}$ and ${\sigma }_{\mathit{sy}}$ are the standard deviations in the data, the standard deviation under the assumption of perfect staggering, and the standard deviation under the assumption of perfect synchronization, respectively.

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Table 3. TAR based unit root test.

	M-TAR based Unit Root Test
	Corn:		Soybeans:
	Futures Price Returns: $\mathrm{\Delta }{p}_{t-1}^f$	Spot Price Returns: $\mathrm{\Delta }{p}_{t-1}^s$	Futures Price Returns: $\mathrm{\Delta }{p}_{t-1}^f$	Spot Price Returns: $\mathrm{\Delta }{p}_{t-1}^s$
Region 1: ($I_t=1$)
${\rho }_1$ (coefficient of lag.price $p_{\mathit{t}-1}$)	0.0300 (0.0210)	−0.0050* (0.0030)	−0.0430* (0.0230)	−0.0070 (0.0080)
constant	−0.1050 (0.068)	0.0110* (0.0060)	0.1560* (0.0840)	0.0140 (0.0160)
Region 2: ($I_t=0$)
${\rho }_2$ (coefficient of lag.price $p_{\mathit{t}-1}$)	−0.0220*** (0.0080)	−0.0210*** (0.0080)	−0.0090 (0.0110)	−0.1030*** (0.0290)
constant	0.0750*** (0.0250)	0.0400** (0.0170)	0.0340 (0.0410)	0.2080*** (0.0580)
F-Test	10.8500***	9.8400***	4.1500**	13.5000***

*** statistically significant at 1% confidence level; **statistically significant at 5% confidence level; * statistically significant at 10% confidence level. The critical values of F-test are obtained from Enders and Granger (1998) and they were found to have better power than the T-test statistics.

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Table 4. Threshold VECM model.

	Asymmetric effects: $\mathrm{\Delta }{p}_t^s=I_t^1{{\alpha }_s}^{-}\mathit{e}{c}_{\mathit{t}-1}+I_t^2{{\alpha }_s}^0\mathit{e}{c}_{\mathit{t}-1}+I_t^3{{\alpha }_s}^{+}\mathit{e}{c}_{\mathit{t}-1}+\sum _{\mathit{i}=1}^k{B}_i\left[\begin{array}{c}\mathrm{\Delta }{p}_{t-i}^f\\ \mathrm{\Delta }{p}_{t-i}^s\end{array}\right]+v_t^s$
	Corn:		Soybeans:
Down interval ($\mathit{e}{c}_{\mathit{t}-1}<{\theta }^{-}$):	${\alpha }_s^{-}$	−0.0340*** (0.0116)	${\alpha }_s^{-}$	0.0211 (0.0280)
Middle interval (${\theta }^{-}<\mathit{e}{c}_{\mathit{t}-1}<{\theta }^{+}$):	${\alpha }_s^0$	−0.0100 (0.0237)	${\alpha }_s^0$	−0.0795** (0.0396)
Up interval ($\mathit{e}{c}_{\mathit{t}-1}>{\theta }^{+}$):	${\alpha }_s^{+}$	−0.0441** (0.0206)	${\alpha }_s^{+}$	−0.1468*** (0.0263)

*** statistically significant at 1% confidence level; **statistically significant at 5% confidence level; * statistically significant at 10% confidence level.

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Table 5. TV-PC-VECM model for corn.

Partial cointegration test for corn futures and spot prices:				Test statistics	p-value
Panel A:
$H_0^R$: residual series follows a pure unit root process (no cointegration)				−20.3200	0.0000***
$H_0^M$: residual series follows a pure AR(1) process (linear cointegration)				−1.0300	0.1526
	Logit model for spot price bubbles
	Bubble	Bubble		Bubble	Bubble
Panel B:
Constant	−1.4892*** (0.5123)	−0.7313*** (0.2644)		−0.9080*** (0.2929)	−0.9100*** (0.2919)
$\mathit{Speculatio}{n}_t$	−0.3999 (0.3466)	−0.6205 (0.4170)		−0.4652 (0.3871)	−0.4660 (0.3882)
$\ln \left(\mathit{Tradevolum}{e}_t\right)$	−0.1724*** (0.0413)	−0.1165*** (0.0361)		−0.1314*** (0.0382)	−0.1310*** (0.0380)
${\alpha }_t^s$	429.1173**** (150.9391)
$b_{1,\mathit{sf},\mathit{t}}$	−10.4752*** (2.1626)
$b_{1,\mathit{ss},\mathit{t}}$	3.3089* (1.6969)
$b_{2,\mathit{sf},\mathit{t}}$	11.4598*** (3.471038)
$b_{2,\mathit{ss},\mathit{t}}$	−18.1662*** (2.4944)
$\mathit{OIR}{F}_t$_stof (response of spot price to futures shocks)		−3.1908 (11.4757)			1.2804 (11.8599)
$\mathit{OIR}{F}_t$_stos (response of spot price to own shocks)				17.4735*** (4.1894)	17.5108*** (4.2307)
Observations	456	456		456	456

*** statistically significant at 1% confidence level; **statistically significant at 5% confidence level; * statistically significant at 10% confidence level. The lag length of price returns are determined by information criteria (AIC).

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Table 6. TV-PC-VECM model for soybeans.

Partial cointegration test for soybeans futures and spot prices:				Test statistics		p-value
Panel A:
$H_0^R$: residual series follows a pure unit root process (no cointegration)				−11.2400		0.0000***
$H_0^M$: residual series follows a pure AR(1) process (linear cointegration)				−0.0000		1.0000
	Logit model for spot price bubbles
	Bubble	Bubble			Bubble	Bubble
Panel B:
Constant	−4.1051*** (0.6487)	−1.9670*** (0.3106)			−2.0238*** (0.3079)	−2.0111*** (0.3102)
$\mathit{Speculatio}{n}_t$	0.0090 (0.0372)	−0.0444 (0.0697)			−0.0426 (0.0607)	−0.0438 (0.0632)
$\ln \left(\mathit{Tradevolum}{e}_t\right)$	0.0158 (0.0636)	−0.0043 (0.0459)			0.0047 (0.0449)	−0.0002 (0.0463)
${\alpha }_t^s$	96.2165 (125.3267)
$b_t^{1,sf}$	9.3231*** (2.9634)
$b_t^{1,ss}$	−6.9644*** (1.4290)
$b_t^{2,sf}$	−7.5480** (2.9519)
$b_t^{2,ss}$	3.3498* (1.7940)
$\mathit{OIR}{F}_t$_stof (response of spot price to futures shocks)		−2.0693 (1.6469)				1.8019 (1.6922)
$\mathit{OIR}{F}_t$_stos (response of spot price to own shocks)					5.3931 (3.7605)	4.8610 (3.8646)
Observations	456	456			456	456

*** statistically significant at 1% confidence level; **statistically significant at 5% confidence level; * statistically significant at 10% confidence level. The lag length of price returns are determined by information criteria (AIC).

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Figure 3. Corn: time-varying long run and short run adjustment parameters for the spot price.

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Figure 4. Soybeans: time-varying long run and short run adjustment parameters for the spot price.

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Figure 5. Corn: time-varying OIRF.

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Figure 6. Soybeans: time-varying OIRF.

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Table A1. Unit root tests.

	Corn:		Soybeans:
	Futures Price:	Spot Price:	Futures Price:	Spot Price:
ADF Test	−2.0840	−1.7720	−1.5140	−1.9610
P-value	0.2510	0.3945	0.5263	0.3037
KPSS Test	1.94	2.0000	1.7	1.78
P-value	0.0100	0.0100	0.0100	0.0100
	Futures Price Returns:	Spot Price Returns:	Futures Price Returns:	Spot Price Returns:
ADF Test	−26.8850	−15.8580	−20.9910	−24.1340
P-value	0.0000	0.0000	0.0000	0.0000
KPSS Test	0.0543	0.0953	0.0335	0.0806
P-value	0.1000	0.1000	0.1000	0.1000

For the ADF test, whether to include the constant term and the number of lags (k = 1 or 2) are determined by AIC. For the KPSS test, the autocovariance function is to be weighted by the quadratic spectral kernel. Automatic bandwidth selection procedure proposed by Newey and West (Newey & West, 1994) is applied here.

Source: Own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Table A2. Cointegration test and granger causality test.

				Trace Test
(5% critical values in the parentheses)				r0	r1
Johansen Cointegration Test:
Corn: Futures and Spot Prices				83.2115 (15.4100)	3.4488 (3.7600)
Soybeans: Futures and Spot Prices				25.1818 (15.4100)	1.2377 (3.7600)
H0 is the null hypothesis. (P-value in the parentheses)					F-statistics
Granger-causality tests:
H0: Corn Spot Price Returns do not Granger-cause Futures Price Returns					0.8302 (0.5496)
H0: Corn Futures Price Returns do not Granger-cause Spot Price Returns					9.9131*** (0.0000)
H0: Soybean Spot Price Returns do not Granger-cause Futures Price Returns					0.0972 (0.9926)
H0: Soybean Futures Price Returns do not Granger-cause Spot Price Returns					2.5440** (0.0276)

*** statistically significant at 1% confidence level; **statistically significant at 5% confidence level; * statistically significant at 10% confidence level.

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Figure A1. Corn: time-varying long run and short run adjustment parameters for the futures price.

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Figure A2. Soybeans: time-varying long run and short run adjustment parameters for the futures price.

Source: own calculations based on data from DCE and the China Grain Reserves Group, Ltd. using Stata 15.

Loy, J.-P., & Weiss, C. (2002). Staggering and synchronisation of prices in a low-inflation environment: Evidence from German food stores. Agribusiness, 18(4), 437–457. https://doi.org/10.1002/agr.10032

 Google Scholar

Enders, W., & Granger, C. W. J. (1998). Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics, 16(3), 304–311. https://doi.org/10.1080/07350015.1998.10524769

 Web of Science ®Google Scholar

Newey, W. K., & West, K. D. (1994). Automatic lag selection in covariance matrix estimation. The Review of Economic Studies, 61(4), 631–653. https://doi.org/10.2307/2297912

 Web of Science ®Google Scholar