# Geographical Indications and Price Volatility Dynamics of Lamb Prices in Spain

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## Abstract

**:**

## 1. Introduction

## 2. The Lamb Sector and the European Food Quality Schemes in Spain

## 3. Methodology

## 4. Data and Results

#### 4.1. PGI Cordero de Navarra

#### 4.2. Non-PGI Cordero de Navarra

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**RPI: Retail prices of Protected Geographical Indication (PGI) lamb (main axis); FPI: Farm prices of the PGI lamb (secondary axis). Prices are expressed in €, and vertical axes are measured in €/kg carcass.

**Figure 2.**RP: Retail prices of the non-PGI lamb (main axis); FP: Farm prices of the non-PGI lamb (secondary axis). Prices are expressed in € and vertical axes are measured in €/kg carcass.

**Figure 3.**(

**a**) Predicted conditional variances at retail price level; (

**b**) predicted conditional variances at farm price level.

**Figure 4.**(

**a**) Predicted conditional variances at retail price level; (

**b**) predicted conditional variances at farm price level.

FPI | RPI | |
---|---|---|

Number of observations | 373 | 373 |

Mean | 6.398 | 11.945 |

Minimum | 5.280 | 10.840 |

Maximum | 7.91 | 12.870 |

Standard deviation | 0.617 | 0.385 |

Test for ARCH effects | 331.812 *** | 317.817 *** |

Linear time trend | −6.7 × 10^{−4} ** | 4.99 × 10^{−4} *** |

PQ (2007) | −16.684 | −14.414 |

KPSS (1992) | 0.423 *** | 2.284 *** |

Rank | Eigenvalue | ${\mathit{\lambda}}_{\mathit{t}\mathit{r}\mathit{a}\mathit{c}\mathit{e}}^{*}$ |
---|---|---|

0 | 0.053 | 29.947 *** |

1 | 0.026 | 9.606 ** |

**Table 3.**Estimated results for VECM–Babba, Engle, Kraft, and Kroner (BEKK)– multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) model for the PGI lamb.

Cointegration Relationship:$RP{I}_{t}={2.184}^{***}+{0.160}^{***}FP{I}_{t}$ | ||

Conditional Mean Equation (VECM): | ||

$\left(\begin{array}{c}\mathsf{\Delta}RP{I}_{t}\\ \mathsf{\Delta}FP{I}_{t}\end{array}\right)=\left(\begin{array}{c}{\alpha}_{1}\\ {\alpha}_{2}\end{array}\right){\epsilon}_{t-1}+\left(\begin{array}{cc}{\delta}_{11}& {\delta}_{12}\\ {\delta}_{21}& {\delta}_{22}\end{array}\right)\left(\begin{array}{c}\mathsf{\Delta}RP{I}_{t-1}\\ \mathsf{\Delta}FP{I}_{t-1}\end{array}\right)+\left(\begin{array}{c}{u}_{1t}\\ {u}_{2t}\end{array}\right)$ | ||

$\mathsf{\Delta}RPPG{I}_{t}$ | $\mathsf{\Delta}FPPG{I}_{t}$ | |

$\mathsf{\Delta}RP{I}_{t-1}$ | 0.091 ** | 0.080 |

$\mathsf{\Delta}FP{I}_{t-1}$ | 0.007 | 0.057 |

${\epsilon}_{t-1}$ | −0.103 *** | 0.040 |

Multivariate ARCH LM test: | 18.49 ** | |

Multivariate Q test: | 45.234 | |

Conditional variance equation (symmetric BEKK–MGARCH): | ||

$\left(\begin{array}{c}{h}_{11}\\ {h}_{22}\end{array}\right)=\left(\begin{array}{cc}{c}_{11}& 0\\ {c}_{12}& {c}_{22}\end{array}\right)\left(\begin{array}{cc}{c}_{11}& {c}_{21}\\ 0& {c}_{22}\end{array}\right)+\left(\begin{array}{cc}{a}_{11}& {a}_{21}\\ {a}_{12}& {a}_{22}\end{array}\right)\left(\begin{array}{c}{u}_{1t-1}^{2}\\ {u}_{2t-1}^{2}\end{array}\right)\left(\begin{array}{cc}{u}_{1t-1}^{2}& {u}_{2t-1}^{2}\end{array}\right)\left(\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right)\phantom{\rule{0ex}{0ex}}+\left(\begin{array}{cc}{b}_{11}& {b}_{21}\\ {b}_{12}& {b}_{22}\end{array}\right)\left(\begin{array}{cc}{h}_{11t-1}& {h}_{12t-1}\\ {h}_{21t-1}& {h}_{22t-1}\end{array}\right)\left(\begin{array}{cc}{b}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right)$ | ||

${c}_{11}$ | 0.011 *** | |

${c}_{21}$ | 0.006 | |

${c}_{22}$ | 0.012 * | |

${a}_{11}$ | 0.039 | |

${a}_{12}$ | −0.028 | |

${a}_{21}$ | −0.105 | |

${a}_{22}$ | 0.107 | |

${b}_{11}$ | 0.271 | |

${b}_{12}$ | −1.795 *** | |

${b}_{21}$ | 0.090 | |

${b}_{22}$ | 0.670 ** | |

Joint stability test: | 4.372 * | |

LR test for the null that ${a}_{ii},{b}_{ii}$ for $i=1,2$ are zero: | 179.416 *** | |

LR test for the null that ${a}_{12},{a}_{21},{b}_{12},{b}_{21}$ are zero (BEKK cross effects): | 31.831 *** |

$\begin{array}{ll}{h}_{11}=1.54\times {10}^{-4}& +0.074{h}_{11t-1}+0.008{h}_{22t-1}+0.049{h}_{12t-1}\\ & +0.002{u}_{1t-1}^{2}+0.011{u}_{2t-1}^{2}-0.008{u}_{1t-1}{u}_{2t-1}\end{array}$ |

$\begin{array}{ll}{h}_{22}=1.45\times {10}^{-4}& +{3.221}^{*}{h}_{11t-1}+0.449{h}_{22t-1}\\ & -{2.404}^{***}{h}_{12t-1}+0.001{u}_{1t-1}^{2}+0.011{u}_{2t-1}^{2}\\ & -0.006{u}_{1t-1}{u}_{2t-1}\end{array}$ |

**Table 5.**Summary of descriptive statistics and univariate nonstationarity tests for the non-PGI lamb.

FP | RP | |
---|---|---|

Number of observations | 373 | 373 |

Mean | 6.086 | 10.607 |

Minimum | 4.950 | 8.840 |

Maximum | 7.450 | 12.250 |

Standard deviation | 0.570 | 0.725 |

ARCH effect test | 338.299 *** | 324.403 *** |

Linear time trend | −2.60×10^{−4} | 0.003 *** |

Perron and Qu (2007) | −5.521 | −17.118 |

KPSS (1992) | 0.695 *** | 2.259 *** |

Rank | Eigenvalue | ${\mathit{\lambda}}_{\mathit{t}\mathit{r}\mathit{a}\mathit{c}\mathit{e}}^{*}$ |
---|---|---|

0 | 0.044 | 25.212 *** |

1 | 0.024 | 8.897 * |

Cointegration Relationship:$\mathit{R}{\mathit{P}}_{\mathit{t}}={\mathbf{1.811}}^{***}+{\mathbf{0.304}}^{***}\mathit{F}{\mathit{P}}_{\mathit{t}}$ | ||

Conditional Mean Equation (VECM): | ||

$\left(\begin{array}{c}\mathsf{\Delta}RPPG{I}_{t}\\ \mathsf{\Delta}FPPG{I}_{t}\end{array}\right)=\left(\begin{array}{c}{\alpha}_{1}\\ {\alpha}_{2}\end{array}\right){\epsilon}_{t-1}+\left(\begin{array}{cc}{\delta}_{111}& {\delta}_{112}\\ {\delta}_{121}& {\delta}_{122}\end{array}\right)\left(\begin{array}{c}\mathsf{\Delta}RPPG{I}_{t-1}\\ \mathsf{\Delta}FPPG{I}_{t-1}\end{array}\right)+\left(\begin{array}{cc}{\delta}_{211}& {\delta}_{212}\\ {\delta}_{221}& {\delta}_{222}\end{array}\right)\left(\begin{array}{c}\mathsf{\Delta}RPPG{I}_{t-2}\\ \mathsf{\Delta}FPPG{I}_{t-2}\end{array}\right)\phantom{\rule{0ex}{0ex}}+\left(\begin{array}{cc}{\delta}_{311}& {\delta}_{312}\\ {\delta}_{321}& {\delta}_{322}\end{array}\right)\left(\begin{array}{c}\mathsf{\Delta}RPPG{I}_{t-3}\\ \mathsf{\Delta}FPPG{I}_{t-3}\end{array}\right)+\left(\begin{array}{c}{u}_{1t}\\ {u}_{2t}\end{array}\right)$ | ||

$\mathsf{\Delta}R{P}_{t}$ | $\mathsf{\Delta}F{P}_{t}$ | |

$\mathsf{\Delta}R{P}_{t-1}$ | −0.049 | 0.014 |

$\mathsf{\Delta}R{P}_{t-2}$ | −0.081 * | 0.016 |

$\mathsf{\Delta}R{P}_{t-3}$ | −0.042 | 0.062 |

$\mathsf{\Delta}F{P}_{t-1}$ | 0.134 *** | 0.130 * |

$\mathsf{\Delta}F{P}_{t-2}$ | 0.094 * | 0.077 ** |

$\mathsf{\Delta}F{P}_{t-3}$ | 0.009 | 0.002 |

${\epsilon}_{t-1}$ | −0.036 ** | 0.005 |

Multivariate ARCH LM test: | 30.96 *** | |

Multivariate Q test: | 0.703 | |

Conditional variance equation (asymmetric BEKK–MGARCH): | ||

$\begin{array}{ll}\left(\begin{array}{c}{h}_{11}\\ {h}_{22}\end{array}\right)& =\left(\begin{array}{cc}{c}_{11}& 0\\ {c}_{12}& {c}_{22}\end{array}\right)\left(\begin{array}{cc}{c}_{11}& {c}_{21}\\ 0& {c}_{22}\end{array}\right)+\left(\begin{array}{cc}{a}_{11}& {a}_{21}\\ {a}_{12}& {a}_{22}\end{array}\right)\left(\begin{array}{c}{u}_{1t-1}^{2}\\ {u}_{2t-1}^{2}\end{array}\right)\left(\begin{array}{cc}{u}_{1t-1}^{2}& {u}_{2t-1}^{2}\end{array}\right)\left(\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right)\\ & +\left(\begin{array}{cc}{b}_{11}& {b}_{21}\\ {b}_{12}& {b}_{22}\end{array}\right)\left(\begin{array}{cc}{h}_{11t-1}& {h}_{12t-1}\\ {h}_{21t-1}& {h}_{22t-1}\end{array}\right)\left(\begin{array}{cc}{b}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right)\\ & +\left(\begin{array}{cc}{d}_{11}& {d}_{21}\\ {d}_{12}& {d}_{22}\end{array}\right)\left(\begin{array}{c}{v}_{1t-1}^{2}\\ {v}_{2t-1}^{2}\end{array}\right)\left(\begin{array}{cc}{v}_{1t-1}^{2}& {v}_{2t-1}^{2}\end{array}\right)\left(\begin{array}{cc}{d}_{11}& {d}_{12}\\ {d}_{21}& {d}_{22}\end{array}\right)\end{array}$ | ||

${c}_{11}$ | 0.0125 *** | |

${c}_{21}$ | 0.004 *** | |

${c}_{22}$ | 0.015 *** | |

${a}_{11}$ | −0.125 *** | |

${a}_{12}$ | −0.461 *** | |

${a}_{21}$ | 0.013 | |

${a}_{22}$ | 0.165 *** | |

${b}_{11}$ | 0.757 *** | |

${b}_{12}$ | −0.176 *** | |

${b}_{21}$ | 0.180 *** | |

${b}_{22}$ | 0.545 *** | |

${d}_{11}$ | 0.288 *** | |

${d}_{12}$ | −0.655 *** | |

${d}_{21}$ | 0.122 ** | |

${d}_{22}$ | 0.107 | |

Joint stability test: | 6.528 * | |

LR test for the null of asymmetric effects | 57.897 *** | |

LR test for the null that ${a}_{ij},{b}_{ij},{d}_{ij}$ for $i,j=1,2$ are zero: | 1828.121 *** | |

LR test for the null that ${a}_{ij},{b}_{ij}$ for $i,j=1,2$ are zero: | 1800.093 *** | |

LR test for the null that ${a}_{ij},{b}_{ij}$ for $i\ne j,i,j=1,2$ are zero (BEKK cross effects): | 47.822 *** |

$\begin{array}{ll}{h}_{11}=1.74\times {10}^{-{4}^{***}}& +{0.573}^{***}{h}_{11t-1}+{0.032}^{***}{h}_{22t-1}+{0.272}^{***}{h}_{12t-1}\\ & +0.016{u}_{1t-1}^{2}+1.66\times {10}^{-4}{u}_{2t-1}^{2}-0.003{u}_{1t-1}{u}_{2t-1}\\ & +{0.083}^{***}{v}_{1t-1}^{2}+0.015{v}_{2t-1}^{2}+{0.104}^{***}{v}_{1t-1}{v}_{2t-1}\end{array}$ |

$\begin{array}{ll}{h}_{22}=2.30\times {10}^{-{4}^{***}}& +{0.031}^{***}{h}_{11t-1}+{0.299}^{***}{h}_{22t-1}-{0.192}^{***}{h}_{12t-1}\\ & +{0.213}^{***}{u}_{1t-1}^{2}+{0.027}^{*}{u}_{2t-1}^{2}-{0.152}^{***}{u}_{1t-1}{u}_{2t-1}\\ & +{0.429}^{***}{v}_{1t-1}^{2}+0.012{v}_{2t-1}^{2}-{0.715}^{***}{v}_{1t-1}{v}_{2t-1}\end{array}$ |

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**MDPI and ACS Style**

Ferrer-Pérez, H.; Abdelradi, F.; Gil, J.M.
Geographical Indications and Price Volatility Dynamics of Lamb Prices in Spain. *Sustainability* **2020**, *12*, 3048.
https://doi.org/10.3390/su12073048

**AMA Style**

Ferrer-Pérez H, Abdelradi F, Gil JM.
Geographical Indications and Price Volatility Dynamics of Lamb Prices in Spain. *Sustainability*. 2020; 12(7):3048.
https://doi.org/10.3390/su12073048

**Chicago/Turabian Style**

Ferrer-Pérez, Hugo, Fadi Abdelradi, and José M. Gil.
2020. "Geographical Indications and Price Volatility Dynamics of Lamb Prices in Spain" *Sustainability* 12, no. 7: 3048.
https://doi.org/10.3390/su12073048