Nonlinear dynamics of pork price in China

Nonlinear dynamics of pork price in China

Journal of Integrative Agriculture 2015, 14(6): 1115–1121 Available online at www.sciencedirect.com ScienceDirect RESEARCH ARTICLE Nonlinear dynami...

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Journal of Integrative Agriculture 2015, 14(6): 1115–1121 Available online at www.sciencedirect.com

ScienceDirect

RESEARCH ARTICLE

Nonlinear dynamics of pork price in China ZHAO Guo-qing, WU Qiong School of Economics, Renmin University of China, Beijing 100872, P.R.China

Abstract This paper primarily analyzes the evolution path of China’s pork price by employing the threshold autoregression model (TAR). Considering the unit root test with a threshold effect and heteroskedasticity of the TAR model, we show that the pork price series is a unit root process in each regime, and the heteroskedasticity in the TAR model greatly affects the results of linearity test. We find that the changing process of pork price has two regimes: mild regime and expansion regime. In particular, a change belongs to an expansion regime if it is larger than 0.5881; otherwise, it falls in the mild regime. Keywords: pork price, heteroskedasticity, TAR unit root

1. Introduction Hog industry plays a pivotal role in China’s economic system, not only because pork is among the most important sources of food in China, but also due to the fact that the changes in pork price significantly affect China’s consumer price index (CPI), which eventually influence the national macroeconomic policy. Even today, the Engel Index in China (share of expenditure on food in total household expenditure) is still as high as 35%. Among all the sources of food, meat is definitely a crucial one. The meat prices have a substantial influence on the CPI. Fig. 1 indicates that pork price had a higher volatility than other meat and food products did. It has been documented that pork accounts for a large proportion of

Received 23 July, 2014 Accepted 28 December, 2014 Correspondence ZHAO Guo-qing, Tel: +86-10-82500714, Fax: +86-10-62511091, E-mail: [email protected]; WU Qiong, E-mail: [email protected] © 2015, CAAS. All rights reserved. Published by Elsevier Ltd. doi: 10.1016/S2095-3119(14)60994-1

meat (more than 60%), so that the pork’s weight could be more than 6% in the calculation of the CPI (Yu and Abler 2014). There is a significant correlation between pork price and the CPI, and the correlation coefficient is as large as 0.82. Therefore, the volatility of pork price may affect the size of the CPI to a substantial extent. Fig. 2 indicates that there were three large price cycles or spikes in China’s pork prices from January 2000 to March 2014. To be more specific, it shows that: (1) The first spike occurred in the period from 2003 to 2006, with pork price increasing from 9.76 CNY kg–1 in May 2003 to 15.13 CNY kg–1 in September 2004 and then decreasing to 10.58 CNY kg–1 in June 2006; (2) the second spike appeared from 2007 to 2009, with pork price increasing from 14.39 CNY kg–1 in April 2007 to 26.08 CNY kg–1 in February 2008 rapidly and then decreasing to 15.46 CNY kg–1 in June 2009; (3) the third spike happened from 2010 to 2012, with pork price increasing from 16.04 CNY kg–1 in June 2010 to 30.35 CNY kg–1 in September 2011 and then decreasing to 22.61 CNY kg–1 in July 2012 (according to the China Animal Agriculture Association (CAAA), CNY kg–1). The three price spikes brought a lot of uncertainties to producers; meanwhile, they caused welfare loss for consumers. Chinese government carried out a series of policies to stabilize the prices, such as various subsidies on hog farmers, which further distorted

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Fig. 2 Price of pork, 2000–2014. The data are from CAAA database.

the other hand, some others use threshold autoregression model (TAR) to analyze the asymmetry of pork price. For instance, Hu and Wang (2010) find that there is a nonlinear adjustment mechanism in China’s pork price index. Yang and Xu (2011) conclude that both hog price and pork price are sensitive to bad news in China. Wang et al. (2014) also find the asymmetric transfer of hog price and pork price. In addition, Luo and Liu (2011) indicate that there is no significant asymmetry of volatility based on threshold autoregressive conditional heteroskedasticity (TARCH) model or exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model, while Feng (2013) obtains an opposite conclusion based on the same method for China’s pork market with different sample period. Although the nonlinear smooth transition characteristics of pork price have been intensively discussed by previous studies, few of them consider the effect of heteroskedasticity in empirical studies. As the sampling distributions are quite sensitive to conditional heteroskedasticity in the errors, modeling the conditional variance more carefully is necessary for accurate inference on the conditional mean (Hansen 1997). The unit root tests, such as the ADF test, have low power if there is a threshold effect. However, the empirical studies of pork prices fail to pay enough attention to these issues. Considering a unit root test with a threshold effect and heteroskedasticity of the TAR model, this paper gives a further empirical analysis about the path of China’s pork price. The empirical results suggest that if the heteroskedasticity of the TAR model is ignored, the path of China’s pork price may have incorrect regimes. Further, the path of China’s pork price has a significant threshold effect so that it can be divided into an expansion regime and a mild regime, which will be defined later. The organization of this paper is as follows. In section 2, the frame of TAR model is discussed, it includes the model estimation and testing method associated with the number of regimes, and then reports an application to China’s pork price data. The estimate results and some discussions are given in sections 3 and 4, respectively. The final section concludes.

the price system, and increased price volatility in contrast.

2. Data and methods

PP

200

CPI

MP

FP

180

Index

160 140 120 100 80

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Fig. 1 Index of pork, meat, food and consumer price, 2001–2014. PP, pork price; CPI, consumer price index; MP, meat price; FP, food price. The data are from China Animal Agriculture Association (CAAA) and National Bureau of Statistics of China (NBSC).

32

Price (CNY kg–1)

28 24 20 16 12

20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 20 08 20 09 20 10 20 11 20 12 20 13

8

Year

Given the important policy implications, a lot of researches have shed light on analyses of pork price. Some previous studies pay attention to the causes of the volatilities of hog and pork prices (Xin and Tan 1999; Li and He 2007; Xu 2008), and recent literatures are mainly focused on whether or not the price transmission and adjustment is asymmetric in the pork market. On the one hand, several studies use the asymmetric error correction model (AECM) to deal with the problem. Yu and Zheng (2013) suggest that there is an asymmetry in the pork price transmission. On

2.1. SETAR(2) and SETAR(3) TAR models can capture the nonlinear characteristics of the system and use the space of threshold to improve the accuracy of the linear approximation (Tsay 1989, 2002; Tong 1990; Chan 1993; Hansen 1996, 1997). A TAR (m) model takes the form (1) Yt=α1TXt–1I1t (γ, d)+...+αmT Xt–1Imt (γ, d)+ut Where, Yt is a univariate time series and Xt–1=(1 Yt–1 Yt–2... Yt–s)T is a k×1 vector with k=1+s; the parameters αi is a k×1

ZHAO Guo-qing et al. Journal of Integrative Agriculture 2015, 14(6): 1115–1121

vector, with i=1, 2, ..., m; γ are called the thresholds and γ=(γ1, ..., γm–1) with γ1<γ2< ...<γm–1; I(•) denotes the indicator function and Ijt (γ, d)=I(γj–1
2.2. Testing for threshold autoregression The null hypothesis H0 is that “the model is SETAR(j)” and the alternative hypothesis H1 is that “the model is SETAR(k)”, where k>j. Thus, the null hypothesis can be rejected for large values of

Fn=n

σ~ n2 − σ^ n2 ( γ) σ^ n2 (γ )

(7)

~2 Where, σ is the residual sum of squares under H0 and n σ (γ) is the residual sum of squares under H1. Since γ is ^2 n

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not well identified under H0, the asymptotic distribution of Fn is not χ2 and the distribution is sensitive to conditional heteroskedasticity in the error (Davies 1977, 1987; Hansen 1997). Hansen (1996, 1997) shows the distribution of Fn and presents a bootstrap method to calculate the critical values in finite samples. Let u*t, t=1, ..., n, be i.i.d. N(0, 1) random draws and set Y *t=u*t. Using the observations Xt, t=1, ..., n, we can regress Y *t on Xt to obtain the residual ~ *2 variance σ , on Xt(γ) to obtain the residual variance σ^ n*2(γ), n and form F n* (γ)=n(σ~ n*2– σ^ n*2(γ))/σ^ n*2(γ) and F n* =suγ pF n* (γ). Hansen (1996) shows that the distribution of F n* converges weakly in probability to the null distribution of Fn. When the error is conditionally heteroskedasticity, it is necessary to replace the F statistic with a Wald statistic. ^ ^ Wn(γ)=(Rθ(γ))T[R(Mn(γ)–1Vn(γ)Mn(γ)–1)RT]–1Rθ(γ) (8) T Where, R=(I –I), Mn(γ)=∑Xt(γ)Xt(γ) ,and Vn(γ)=∑Xt(γ)Xt(γ)Tu^ 2t. Let Wn=suγ p Wn(γ) so the bootstrap method can be used to get the critical values of Fn and Wn.

2.3. Data There are three sets of prices related to pork price in China: piglet price, hog price and pork price, as shown in Fig. 3. The time period is from January 2000 to March 2014. According to Fig. 3, the three price series are very similar in fluctuations. Since Chinese government pays more attention to pork price and it is a big chunk of the CPI basket, we use the pork price in our study. The highest price is 30.35 CNY kg–1 in September 2011, and the lowest price is 9.47 CNY kg–1 in June 2000; the average price is 16.9 CNY kg–1; the standard deviation is about 6.06 in sample period (according to the CAAA, CNY kg–1). The pork price may exert some seasonality properties, so the Census X12 method is used to adjust seasonal fluctuation. The data are obtained from the CAAA.

2.4. Testing Since the assumptions of SETAR models require that the series and the thresholds must be stationary, the first step is to test the stationary of the series. If the series has a threshold effect, the ADF test and PP test have low powers; or, high powers (Pippenger and Goering 1993; Balke and Fomby 1997; Enders and Granger 1998; Enders 2001). Caner and Hansen (2001) find that the distributions of tests for an autoregressive unit root are nonstandard and dependent on the presence of a threshold effect. They give a bootstrap method to test the unit root with a threshold effect. Compared with the ADF test, the bootstrap method they mentioned has more power. Since the presence of a threshold effect in the pork price is unknown, we use both the ADF test and the method proposed by Caner and Hansen to

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LP

40

PP

Table 1 Unit root tests1)

HP

ADF ADF

Price (CNY kg–1)

35 30

KPSS KPSS

25

1) 2)

20

Variable Y ΔY Variable Y ΔY

(c, t, s)2) (1, 1, 13) (0, 0, 13) (c, t, b)2) (1, 1, 74.2) (1, 0, 9.23)

t-statistic 5% critical value –2.9314 –3.4366 –6.6096** –1.9427 LM statistic 5% critical value 0.1622** 0.1460 0.0543 0.4630

ADF test, H0 is a unit root; KPSS test, H0 is stationarity. c, the intercept; t, time trend; s, lag length; 1, include, 0, exclude for (c, t, s); b is bandwidth for (c, t, b).

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Table 2 Unit root tests for threshold effect1)

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00

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Year

Statistics2) R2T R1T –t1 –t2

Value 0.8610 0.4992 0.7065 –0.6015

5% critical value of bootstrap 12.7438 11.9228 2.9806 2.8201

P-value 0.886 0.884 0.613 0.888

1)

Fig. 3 Price of piglet, pork and hog, 2000–2014. LP, piglet price; HP, hog price. The data are from CAAA database.

test the stationarity of Y. As a complementary of the ADF test, which might have a low power, the KPSS method is also performed to test the stationarity of the series. The null hypothesis of the ADF test is that the series is nonstationary, while the null hypothesis of the KPSS test is that the time series is stationary. According to the method proposed by Caner and Hansen (2001), the model which was used to test unit root with a threshold effect can be written as: ΔYt=θT1Xt–1I(ΔYt–d≤γ)+θT2Xt–1I(ΔYt–d>γ)+et (9) Where, Xt–1=(Yt–1 rTt ΔYt–1 ... Yt–s)T, t=1,…,T, in which rt is a vector of deterministic components including an intercept and possibly a linear time trend; θ1=(ρ1 β1 αT1)T; and θ2=(ρ2 β2 αT2)T; β1 and β2 have the same dimension as rt, and α1 and α2 are s-vectors . If there is a threshold effect, then the null hypothesis is H0: ρ1=ρ2=0 and the alternative hypothesis is H1: ρ1<0 and ρ2<0. The results of the ADF test, KPSS test and unit root test with a threshold effect are presented in Tables 1 and 2, respectively. As shown in Tables 1 and 2, the variable Y has a unit root and the values of –t1 and –t2 are 0.7065 and –0.6015, both are less than the critical value of bootstrap. Therefore, China’s pork price exhibits a unit root property in each regime. To ensure stationary, the first-differenced series of pork price ΔY is used to analyze.

3. Results Using the methods mentioned above, we can estimate the parameters of SETAR(2) and SETAR(3), ensuring that the subsample is more than 15% of the total sample in each

For the unit root test with a threshold effect, when d=8, the F statistic is maximum, and the maximum is 59.38, so we let d=8. 2) R2T and R1T are the statistics under H0; –t1 and –t2 are the t statistics corresponding to the ρ^ 1 and ρ^ 2 in eq. (9), that can be used to test the partial unit root process. Please refer to Caner and Hansen (2001) for more details.

regime. Before estimating the delay parameter d and the threshold value γ, we must obtain the autoregressive lag order s in each regime. We find that the Akaike information criterion (AIC) can be minimized in the linear AR model when s equals 13 and the minimal AIC is 1.89. Hence, we set s=13 in SETAR(2) and SETAR(3). Then, for SETAR(2) and SETAR(3), d and γ can be estimated by the grid search method and the procedure proposed by Bai and Perron (1998) respectively. For SETAR(2), we find that the sum of squared errors (eq. (4)) can be minimized, so that the F statistic can be maximized when d equals 8 and the threshold value is 0.5881. The corresponding value of the F statistic is 59.38. For SETAR(3), we obtain the following estimates: ^ d=8, γ^ 1=–0.1414 and γ^ 2=0.5881. The estimation results of SETAR(2) and SETAR(3) are presented in Tables 3 and 4, respectively. The estimation of SETAR(2) and SETAR(3) are insufficient to conclude which model can describe China’s pork price properly nor whether the nonlinear models are superior to linear ones. As a result, the number of regimes, namely “SETAR(1) against SETAR(2)”, “SETAR(1) against SETAR(3)”, and “SETAR(2) against SETAR(3)”, must be tested. When testing a linear model against a nonlinear model, the distribution of the test statistic depends on the error of SETAR(1). To assess the presence of conditional heteroskedasticity, we regress the squared residual on squares of the regressors. Then the Wald statistic can be used to test the joint significance of the regressors, and the value of the Wald statistic is 131.79 with P-value 0.00. Thus, we can confirm that the error of SETAR(1) does

ZHAO Guo-qing et al. Journal of Integrative Agriculture 2015, 14(6): 1115–1121

Table 3 Estimated SETAR(2)

Table 4 Estimated SETAR(3)

Variable

ΔYt–8≤0.5881

ΔYt–8>0.5881

Intercept

0.0869** (0.0419) 0.3946*** (0.0798) –0.4013*** (0.1340) 0.2345** (0.1016) –0.04849 (0.1581) –0.0095 (0.1298) 0.0893 (0.1156) 0.0274 (0.1143) 0.1187 (0.0965) 0.1147 (0.1013) 0.1083 (0.1048) –0.0153 (0.0907) –0.0387 (0.1019) –0.2908** (0.1172)

0.2994* (0.1568) 1.1036*** (0.1313) 0.012 (0.1189) 0.0144 (0.0809) –0.1458 (0.1006) –0.0576 (0.1127) –0.1709 (0.1246) 0.3900*** (0.1167) –0.4837*** (0.1380) 0.0210 (0.0790) 0.0358 (0.1400) 0.3894*** (0.1087) –0.2723** (0.1125) 0.2585** (0.1073)

ΔYt–1 ΔYt–2 ΔYt–3 ΔYt–4 ΔYt–5 ΔYt–6 ΔYt–7 ΔYt–8 ΔYt–9 ΔYt–10 ΔYt–11 ΔYt–12 ΔYt–13

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Variable ΔYt–8≤–0.1414 Intercept ΔYt–1 ΔYt–2 ΔYt–3 ΔYt–4 ΔYt–5 ΔYt–6 ΔYt–7 ΔYt–8 ΔYt–9 ΔYt–10 ΔYt–11 ΔYt–12 ΔYt–13

0.1732** (0.0790) 0.4311*** (0.1208) –0.2114* (0.1266) 0.2940* (0.1622) 0.1520 (0.1980) –0.2459 (0.1524) 0.1121 (0.1641) 0.0289 (0.1353) 0.1535 (0.1592) 0.4566*** (0.0982) –0.1922 (0.1225) –0.0364 (0.0962) –0.0819 (0.1038) –0.0185 (0.1128)

–0.1414<ΔYt–8≤0.5881

ΔYt–8>0.5881

–0.0026 (0.0556) 0.5204*** (0.0918) –0.5811*** (0.1349) 0.3101*** (0.0950) –0.1473 (0.1659) 0.1143 (0.1313) 0.1628 (0.1370) –0.1073 (0.1489) 0.6122*** (0.2516) –0.2991 (0.1911) 0.2679** (0.1335) 0.1783 (0.1146) –0.0897 (0.1784) –0.3463 (0.2652)

0.2994* (0.1568) 1.1036*** (0.1313) 0.0128 (0.1189) 0.0144 (0.0809) –0.1458 (0.1006) –0.0576 (0.1127) –0.1709 (0.1246) 0.3900*** (0.1167) –0.4837*** (0.1380) –0.0210 (0.0790) 0.0358 (0.1400) 0.3894*** (0.1087) –0.2723** (0.1125) 0.2585** (0.1073)

Standard errors are in parentheses. *, **, and ***, significance at the 10, 5, and 1% levels, respectively. The same as below.

exhibit heteroskedasticity. If we test “SETAR(1) against SETAR(2)”, the value of F statistic is F12=73.86. The corresponding P-value is 0.04 which is estimated from the heteroskedasticity bootstrap method. Then we claim that China’s pork price is a SETAR(2) process. When testing “SETAR(1) against SETAR(3)”, the value of F statistic is F13=128.83. When we use the heteroskedasticity bootstrap method, the P-value is 0.24. Therefore, we cannot reject the null hypothesis, and the result supports that China’s pork price is a SETAR(1) process at the significant level of 5%. However, if the heteroskedasticity is ignored, then the P-value is 0.02. That is, China’s pork price is a SETAR(3) process under this assumption. In conclusion, we suggest that the test results for China’s pork price are sensitive to heteroskedasticity. The test results show that ΔY may be a SETAR(2) process. To verify this finding, we test “SETAR(2) against SETAR(3)”. Before performing the test, we first consider the heteroskedasticity of SETAR(2). We assess this through an OLS regression of the squared LS residual on the squares of the lagged dependent variable and on dummy variables indicating the regimes. Then the value of F statistic is

32.45, and the P-value is 0.00. Thus, we can confirm that the SETAR(2) model does exhibit heteroskedasticity. The F statistic of testing “SETAR(2) against SETAR(3)” is F23=37.39 and the P-value calculated by heteroskedasticity

bootstrap method is 0.23. Therefore, we do not reject the null hypothesis and confirm that China’s pork price is a SETAR(2) process.

4. Discussion The above tests indicate that China’s pork price series can be divided into two regimes. The price belongs to the mild regime if the change in pork price is less than or equal to 0.5881; the price falls in expansion regime if the change in pork price is greater than 0.5881. The two regimes could be interpreted by market behaviors of consumers and producers, as well as by government interventions. When the price change is small, the producers could bear the market risks. However, once the price change is large enough to make hog farmers more profitable or unprofitable, the regime will be switched to the expansion regime. In this regime, farmers may modify the number of sows, and governments may implement policies to intervene the market. The expansion regime is also sensitive to external shocks,

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such as disease and untimely intervenes from government, which lead the pork price to fluctuate fiercely. Further, we use a Wald statistic to test the restrictions that make the parameters in each regime equal and the value of the Wald statistic is 59.00 with the P-value calculated by bootstrap method of 0.005. Therefore, the results support that the change in pork price in each regime reacts differently and the pork price exhibits an obvious nonlinear characteristic. Table 3 indicates that the coefficient of intercept is bigger in the expansion regime than in the mild regime. That is, if the change in pork price enters the expansion regime, the price level will rise dramatically. Most of the absolute values of the parameters in the expansion regime are greater than those in the mild regime, indicating that the reflection of the change of pork price in the expansion regime is longer than in the mild regime. That is to say, the pork price has some inertia during the rising time, as shown in Fig. 4. If the price is in the expansion regime, the hog farmers might increase their supply for more profits by keeping more piglets to grow into sows. However it takes about 8 mon for piglets to grow into sows, and another 5 mon from weaning to fatting and slaughter. As a result, the actions of hog farmers may temporally decrease supply and induce rising pork price in the short run. Under this circumstance, if the government intervenes in the pork market when the price is high, the price cannot be reduced immediately to the mild regime.

5. Conclusion The path of China’s pork price is analyzed in this study

DY

3

TV

2 1 0 –1

20

20

20

20

00 01

02

0 20 3 04 20 05 20 06 20 07 20 08 20 09 20 10 20 1 20 1 12 20 13

–2

based on a SETAR model. The empirical results show that China’s pork price has a unit root process in each regime. The change of pork price is a SETAR(2) process. The price is in the mild regime if the change of pork price is less than or equal to 0.5881; the price is in the expansion regime if the change of pork price is greater than 0.5881. China’s pork price series exhibits strong nonlinear properties which last longer in the expansion regime. Also, it has been shown that employing TAR model without considering the heteroskedasticity in pork price series largely affects the test results. In particular, failing to solve the heteroskedasticity issue could yield misspecification of the threshold parameters, and reduce the prediction accuracy of the model. Volatility of pork price could differ cross periods. To be more specific, price fluctuations are smaller in the mild regime, and the corresponding impact on economy growth is relatively trifling, whereas the expansion regime is generally associated with greater price fluctuations, which is prolonged and could induce market price distortions. Since pork has a high weight in the CPI, the volatility of pork price is influential on China’s inflation calculation. In the latter case, large volatility in pork price might cause abnormal fluctuations in the CPI, and markedly affect how government sets its target of monetary policy. In order to reduce the adverse effects of high fluctuations in pork price, government should maintain a relatively stable level of pork price. Timing of government’s intervention is the key in successful price stabilizing. In other words, untimely intervention of pork market might cause larger price volatility. The empirical results in this paper show that the reflection of the change in pork price is prolonged in the expansion regime than in the mild regime. Therefore, the government should pay close attention to the cycle of pork price when policies are implemented to stabilize the pork price. In other words, the TAR model can be considered as one of the tools of government to monitor pork price. If the change in pork price is greater than the threshold value, it may indicate that there is a shortage of pork supply in the market, and the pork price will keep rising in the next few months. In sum, the government should aim at identifying and analyzing the path of pork volatility properly and employ policies with sufficient foresight to minimize the cost of any inopportune intervention. Results in this paper could shed new light on both of the above aspects, and provide suggestions to the government and other decision-makers.

Acknowledgements

Year

Fig. 4 The regime of pork price. TV, threshold value. DY=ΔYt=Yt–Yt–1.

This study was supported by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University, China (12XNK015).

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References Andrews D W K. 1993. Tests for parameter instability and structural change with unknown change point. Econometrica, 61, 821–856. Bai J. 1997. Estimating multiple breaks one at a time. Econometric Theory, 13, 315–352. Bai J, Perron P. 1998. Estimating and testing linear models with multiple structural changes. Econometrica, 66, 47–78. Balke N S, Fomby T B. 1997. Threshold cointegration. International Economic Review, 38, 627–645. Caner M, Hansen B E. 2001. Threshold autoregression with a unit root. Econometrica, 69, 1555–1596. Chan K S. 1993. Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. Annals of Statistics, 21, 520–533. Davies R B. 1977. Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 64, 247–254. Davies R B. 1987. Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 74, 33–43. 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, 304–311. Enders W. 2001. Improved critical values for the EndersGranger unit-root test. Applied Economics Letters, 8, 257–261. Feng M. 2013. The asymmetric volatility of pork price and its impact on CPI. Statistical Research, 8, 63–68. (in Chinese) Hansen B E. 1996. Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica, 64, 413–430. Hansen B E. 1997. Inference in TAR models. Studies in Nonlinear Dynamics and Econometrics, 2, 1–14. Hu X, Wang J. 2010. Threshold effects of China’s pork price index and policy analysis. Journal of Agrotechnical

1121

Economics, 7, 13–21. (in Chinese) Li B, He Q. 2007. Analysis on the short-term fluctuations of pork price and its reasons in China. Issues in Agricultural Economy, 10, 18–21. (in Chinese) Luo W, Liu R. 2011. Analysis of meat price volatility in China. China Agricultural Economic Review, 3, 402–411. Pippenger M K, Goering G E. 1993. A note on the empirical power of unit root tests under threshold processes. Oxford Bulletin of Economics and Statistics, 55, 473–481. Tong H. 1990. Non-linear Time Series: A Dynamical System Approach. Oxford University Press, Oxford. pp. 194–197. Tsay R S. 1989. Testing and modeling threshold autoregressive processes. Journal of the American Statistical Association, 84, 231–240. Tsay R S. 2002. Analysis of Financial Time Series. John Wiley and Sons, New York. pp. 129–133. Wang J, Qian X, Chen Y. 2014. Research on asymmetric price transmission in the pig industry chain: Empirical analysis based on threshold error correction model. Journal of Agrotechnical Economics, 2, 85–95. (in Chinese) Xin X, Tan X. 1999. Measure of factors influencing volatility of Chinese pigs and pork price. Chinese Rural Economy, 5, 28–34. (in Chinese) Xu X. 2008. The causes of pork prices increase and its impact on macroeconomic. Journal of Agrotechnical Economics, 3, 4–9. (in Chinese) Yang C, Xu X. 2011. Asymmetric transfer of Chinese hog and pork prices. Journal of Agrotechnical Economics, 9, 58–64. (in Chinese) Yu A, Zheng S. 2013. Research on the asymmetric price transfer in China’s pork industry chain. Journal of Agrotechnical Economics, 9, 35–41. (in Chinese) Yu X H. 2014. Monetary easing policy and long-run food prices: Evidence from China. Economic Modelling, 40,175–183. Yu X H, Abler D. 2014. Where have all the pigs gone? Inconsistencies in pork statistics in China. China Economic Review, 30, 469–484. (Managing editor WENG Ling-yun)