# Latin American Agri-Food Exports, 1994–2019: A Gravity Model Approach

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Evolution of Agri-Food Exports from Latin America, 1994–2019

#### 2.2. Theoretical Framework: Gravity Models and the Determinants of International Trade

_{ij}are trade costs between countries i and j; ${\mathrm{Y}}_{\mathrm{i}}$ is the production in country i; ${\mathrm{E}}_{\mathrm{j}}$ is total expenditure of country j; ϵ is the trade elasticity; ${\Pi}_{\mathrm{i}}$ and ${\mathrm{P}}_{\mathrm{j}}$ are the exporter and importer price indexes that aggregate the trade costs over all trading partners.

#### 2.3. Methods of Estimation

#### 2.4. Empirical Model and Data

## 3. Results and Discussion

^{2}between 0.74 and 0.86).

## 4. Sensitivity Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Variables | Obs. | Mean | Std. Dev. | Minimum | Maximum |
---|---|---|---|---|---|

X_{ij,t} | 72,150 | 53,800,000 | 475,000,000 | 0 | 3.19 × 10^{10} |

Dist_{ij} | 71,595 | 10,242 | 4321 | 181.113 | 19,812.040 |

Y_{i,t} | 72,150 | 223,000,000 | 423,000,000 | 3,432,357 | 2.48 × 10^{9} |

Y_{j,t} | 71,340 | 293,000,000 | 1.27 × 10^{9} | 10,887 | 2.14 × 10^{10} |

GAP_{i,t} | 68,265 | 20,200,000 | 38,200,000 | 133,753 | 2.5 × 10^{8} |

Excvol_{ij,t} | 61,790 | 0.412 | 0.673 | 0 | 4.504 |

Polconv_{i,t} | 72,150 | 0.480 | 0.206 | 0 | 0.782 |

Lang_{ij} | 71,595 | 0.109 | 0.312 | 0 | 1 |

Comrelig_{ij,t} | 69,810 | 0.282 | 0.320 | 0 | 0.940 |

Landlocked_{i} | 72,150 | 0.133 | 0.340 | 0 | 1 |

RTA_{ij,t} | 71,595 | 0.126 | 0.320 | 0 | 1 |

WTO_{ij,t} | 71,595 | 0.751 | 0.432 | 0 | 1 |

NAFTA_{ij,t} | 72,150 | 0.001 | 0.027 | 0 | 1 |

MERCOSUR_{ij,t} | 72,150 | 0.004 | 0.066 | 0 | 1 |

CACM_{ij,t} | 72,150 | 0.007 | 0.084 | 0 | 1 |

CAN_{ij,t} | 72,150 | 0.004 | 0.068 | 0 | 1 |

APEC_{ij,t} | 72,150 | 0.018 | 0.133 | 0 | 1 |

ALADI_{ij,t} | 72,150 | 0.028 | 0.165 | 0 | 1 |

G-3_{ij,t} | 72,150 | 0.001 | 0.025 | 0 | 1 |

AP_{ij,t} | 72,150 | 0.001 | 0.026 | 0 | 1 |

P4_{ij,t} | 72,150 | 0 | 0.020 | 0 | 1 |

TPP_{ij,t} | 72,150 | 0.001 | 0.043 | 0 | 1 |

$\mathbf{ln}\left({\mathbf{X}}_{\mathbf{ij},\mathbf{t}}\right)$ | $\mathbf{ln}\left({\mathbf{Y}}_{\mathbf{i},\mathbf{t}}\right)$ | $\mathbf{ln}\left({\mathbf{GAP}}_{\mathbf{i},\mathbf{t}}\right)$ | $\mathbf{ln}\left({\mathbf{Y}}_{\mathbf{j},\mathbf{t}}\right)$ | $\mathbf{ln}\left({\mathbf{Dist}}_{\mathbf{ij}}\right)$ | $\mathbf{ln}\left({\mathbf{Excvol}}_{\mathbf{ij},\mathbf{t}}\right)$ | $\mathbf{ln}\left({\mathbf{Polconv}}_{\mathbf{i},\mathbf{t}}\right)$ | |
---|---|---|---|---|---|---|---|

$\mathbf{ln}\left({\mathbf{X}}_{\mathbf{ij},\mathbf{t}}\right)$ | 1 | ||||||

$\mathbf{ln}\left({\mathbf{Y}}_{\mathbf{i},\mathbf{t}}\right)$ | 0.2889 * | 1 | |||||

$\mathbf{ln}\left({\mathbf{GAP}}_{\mathbf{i},\mathbf{t}}\right)$ | 0.3025 * | 0.9336 * | 1 | ||||

$\mathbf{ln}\left({\mathbf{Y}}_{\mathbf{j},\mathbf{t}}\right)$ | 0.4996 * | 0.0658 * | 0.0580 * | 1 | |||

$\mathbf{ln}\left({\mathbf{Dist}}_{\mathbf{ij}}\right)$ | −0.1504 * | 0.0279 * | 0.0228 * | 0.0889 * | 1 | ||

$\mathbf{ln}\left({\mathbf{Excvol}}_{\mathbf{ij},\mathbf{t}}\right)$ | 0.0499 * | −0.0006 | 0.0187 * | −0.0331 * | 0.0268 * | 1 | |

$\mathbf{ln}\left({\mathbf{Polconv}}_{\mathbf{i},\mathbf{t}}\right)$ | 0.0983 * | 0.1314 * | 0.1791 * | −0.0396 * | 0.0176 * | −0.0470 * | 1 |

VARIABLES | VIF |
---|---|

Log of Exporter GDP (ln Y_{i,t}) | 13.67 |

Log of Exporter GAP (ln GAP_{i,t}) | 12.35 |

Log of Distance (ln Dist_{ij}) | 2.60 |

Common Language (Lang_{ij}) | 1.90 |

ALADI | 1.62 |

RTA | 1.62 |

Exporter Landlocked (Landlocked_{i}) | 1.51 |

Log of Common Religion Index (ln Comrelig_{ij,t}) | 1.41 |

Log of Importer GDP (ln Y_{j,t}) | 1.36 |

CACM | 1.29 |

APEC | 1.26 |

TPP | 1.24 |

CAN | 1.16 |

MERCOSUR | 1.16 |

AP | 1.13 |

WTO | 1.09 |

Log of Exporter Polconv (ln Polconv_{i,t}) | 1.08 |

Log of Excvol (ln Excvol_{ij,t}) | 1.08 |

NAFTA | 1.08 |

G-3 | 1.03 |

P4 | 1.03 |

Dependent Variable: Latin American Agricultural Exports | ||||
---|---|---|---|---|

Explanatory Variables | (Model 1) | (Model 2) | (Model 3) | (Model 4) |

ln Y_{i,t} | 0.0144 | 0.1201 | ||

(0.092) | (0.081) | |||

ln GAP_{i,t} | 0.2474 *** | 0.1906 ** | ||

(0.094) | (0.093) | |||

ln Y_{j,t} | 0.9223 *** | 0.9182 *** | 0.8934 *** | 0.8989 *** |

(0.137) | (0.135) | (0.141) | (0.138) | |

ln Dist_{ij} | −1.6904 *** | −1.7167 *** | −1.1110 *** | −1.0531 *** |

(0.238) | (0.255) | (0.176) | (0.185) | |

RTA_{ij,t} | 0.7024 *** | 0.7136 *** | ||

(0.153) | (0.157) | |||

WTO_{ij,t} | 0.1269 | 0.1085 | 0.1271 | 0.1146 |

(0.167) | (0.164) | (0.162) | (0.161) | |

Lang_{ij} | 0.4314 * | 0.4229 * | 0.7414 *** | 0.7661 *** |

(0.232) | (0.233) | (0.163) | (0.160) | |

Landlocked_{i} | 0.0550 | −0.0123 | 0.0790 | −0.0487 |

(0.317) | (0.316) | (0.268) | (0.256) | |

ln Excvol_{ij,t} | −0.0658 ** | −0.0657 ** | −0.0652 *** | −0.0600 *** |

(0.028) | (0.029) | (0.022) | (0.023) | |

ln Polconv_{i,t} | 0.0560 | 0.0642 | 0.0318 | 0.0415 |

(0.049) | (0.058) | (0.029) | (0.030) | |

NAFTA_{ij,}_{t} | 2.2986 *** | 2.3699 *** | ||

(0.367) | (0.378) | |||

MERCOSUR_{ij,t} | 0.6643 *** | 0.6631 *** | ||

(0.190) | (0.190) | |||

CACM_{ij,t} | 1.0730 ** | 1.2089 ** | ||

(0.481) | (0.511) | |||

CAN_{ij,t} | 0.3270 | 0.3542 | ||

(0.369) | (0.373) | |||

APEC_{ij,t} | 0.5255 ** | 0.5466 ** | ||

(0.233) | (0.238) | |||

ALADI_{ij,t} | 0.0802 | 0.0639 | ||

(0.207) | (0.212) | |||

G-3_{ij,t} | 0.1925 | 0.1689 | ||

(0.334) | (0.335) | |||

AP_{ij,t} | −0.0319 | −0.0641 | ||

(0.222) | (0.222) | |||

P4_{ij,t} | −0.4451 | −0.4033 | ||

(0.332) | (0.343) | |||

TPP_{ij,t} | 0.4731 *** | 0.4584 *** | ||

(0.080) | (0.081) | |||

Constant | 8.9303 *** | 8.8902 *** | 3.3598 * | 3.0362 |

(2.577) | (2.648) | (1.805) | (1.859) | |

Observations | 60,971 | 57,434 | 60,971 | 57,434 |

R-squared | 0.743 | 0.746 | 0.86 | 0.867 |

RESET test (statistic) | 5.28 ** | 4.77 ** | 0.02 | 0.02 |

OLS Model | Heckman Model | |||||
---|---|---|---|---|---|---|

$\mathbf{ln}\left({\mathbf{X}}_{\mathbf{ij},\mathbf{t}}\right)$ | $\mathbf{ln}\left({1+\mathbf{X}}_{\mathbf{ij},\mathbf{t}}\right)$ | Probit | $\mathbf{ln}\left({\mathbf{X}}_{\mathbf{ij},\mathbf{t}}\right)$ | Probit | $\mathbf{ln}\left({\mathbf{X}}_{\mathbf{ij},\mathbf{t}}\right)$ | |

Explanatory Variables | (1) | (2) | (3) | (4) | (5) | (6) |

ln GAP_{i,t} | 0.2861 *** | 0.5988 *** | 0.1841 *** | 0.2903 *** | 0.1695 *** | 0.2657 *** |

(0.056) | (0.099) | (0.039) | (0.056) | (0.039) | (0.056) | |

ln Y_{j,t} | 0.5229 *** | 1.2419 *** | 0.3112 *** | 0.5406 *** | 0.3185 *** | 0.5245 *** |

(0.065) | (0.127) | (0.048) | (0.065) | (0.050) | (0.067) | |

ln Dist_{ij} | −1.8679 *** | −3.4592 *** | −1.1297 *** | −1.8971 *** | −1.1395 *** | −1.9018 *** |

(0.134) | (0.235) | (0.083) | (0.137) | (0.083) | (0.137) | |

WTO_{ij,}_{t} | 0.0947 | 0.0268 | −0.0039 | 0.0940 | −0.0219 | 0.1176 |

(0.101) | (0.170) | (0.063) | (0.101) | (0.067) | (0.107) | |

Lang_{ij} | 0.8656 *** | 2.1703 *** | 0.5723 *** | 0.8902 *** | 0.5606 *** | 0.8773 *** |

(0.199) | (0.428) | (0.212) | (0.199) | (0.211) | (0.198) | |

Landlocked_{i} | −2.8294 *** | −6.1035 *** | −0.8553 *** | −0.8290 *** | −0.9470 *** | −0.7986 *** |

(0.239) | (0.429) | (0.083) | (0.170) | (0.093) | (0.175) | |

ln Excol_{ij,t} | −0.0536 *** | −0.0698 ** | −0.0301 ** | −0.0558 *** | −0.0269 ** | −0.0425 ** |

(0.019) | (0.033) | (0.013) | (0.019) | (0.013) | (0.019) | |

ln Polconv_{i,t} | 0.0214 | −0.0125 | −0.0310 | −0.0258 | 0.0142 | |

(0.028) | (0.055) | (0.023) | (0.024) | (0.027) | ||

ln Comrelig_{ij,t} | 0.1532 ** | |||||

(0.069) | ||||||

NAFTA_{ij,}_{t} | 0.3189 | −0.1126 | 2.2255 *** | 0.3068 | 2.1658 *** | 0.2879 |

(0.426) | (0.555) | (0.447) | (0.425) | (0.447) | (0.423) | |

MERCOSUR_{ij,t} | 0.5039 | −1.2989 | −1.0291 *** | 0.4645 | −1.0060 *** | 0.4820 |

(0.535) | (1.056) | (0.379) | (0.539) | (0.379) | (0.540) | |

CACM_{ij,t} | 1.6248 *** | 0.9879 | −0.6554 * | 1.6131 *** | −0.6836 * | 1.5648 *** |

(0.383) | (0.680) | (0.377) | (0.386) | (0.375) | (0.385) | |

CAN_{ij,t} | 1.0573 ** | 1.2618 | 5.1982 *** | 1.0617 ** | 5.1955 *** | 1.0756 *** |

(0.414) | (0.799) | (0.416) | (0.418) | (0.413) | (0.413) | |

APEC_{ij,t} | 0.9222 *** | 0.8703 *** | 0.4607 * | 0.9187 *** | 0.4176 * | 0.8699 *** |

(0.143) | (0.294) | (0.242) | (0.143) | (0.244) | (0.140) | |

ALADI_{ij,t} | 1.1758 *** | 1.1064 * | 0.7494 *** | 1.1694 *** | 0.7638 *** | 1.1911 *** |

(0.207) | (0.400) | (0.249) | (0.208) | (0.248) | (0.208) | |

G-3_{ij,t} | −0.4509 | −0.0218 | 4.5014 *** | −0.4504 | 4.3874 *** | −0.4961 |

(0.406) | (1.007) | (0.443) | (0.411) | (0.445) | (0.409) | |

AP_{ij,t} | 0.0196 | −0.6304 | 2.8839 *** | 0.0123 | 2.7866 *** | −0.0019 |

(0.231) | (0.504) | (0.376) | (0.233) | (0.386) | (0.231) | |

P4_{ij,t} | −0.5512 | −2.7721 *** | −1.1329 *** | −0.5789 | −1.1259 *** | −0.5459 |

(0.405) | (0.859) | (0.244) | (0.406) | (0.247) | (0.405) | |

TPP_{ij,t} | 0.0409 | −0.6407 ** | −0.6413 ** | 0.0312 | −0.6307 ** | 0.0660 |

(0.137) | (0.287) | (0.308) | (0.137) | (0.309) | (0.131) | |

Constant | 9.0099 *** | 37.3730 *** | 8.9673 *** | 12.0044 *** | 9.3722 *** | 12.1274 *** |

(1.354) | (2.477) | (0.822) | (1.483) | (0.838) | (1.477) | |

Observations | 35,493 | 57,434 | 57,434 | 57,434 | 54,595 | 54,595 |

R-squared | 0.708 | 0.693 | ||||

WALD test | 13.04 *** | 7.73 *** |

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## Share and Cite

**MDPI and ACS Style**

Ayuda, M.-I.; Belloc, I.; Pinilla, V.
Latin American Agri-Food Exports, 1994–2019: A Gravity Model Approach. *Mathematics* **2022**, *10*, 333.
https://doi.org/10.3390/math10030333

**AMA Style**

Ayuda M-I, Belloc I, Pinilla V.
Latin American Agri-Food Exports, 1994–2019: A Gravity Model Approach. *Mathematics*. 2022; 10(3):333.
https://doi.org/10.3390/math10030333

**Chicago/Turabian Style**

Ayuda, María-Isabel, Ignacio Belloc, and Vicente Pinilla.
2022. "Latin American Agri-Food Exports, 1994–2019: A Gravity Model Approach" *Mathematics* 10, no. 3: 333.
https://doi.org/10.3390/math10030333