# Spatial Spillover Effects of Agricultural Transport Costs in Peru

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## Abstract

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## 1. Introduction

## 2. Theoretical Setting

#### 2.1. Agricultural Transport Costs Model

_{od}in kilometres. The price per ton of a good in locations o and d is P

_{o}and P

_{d}, respectively; and the tonnage of a good in each location o and d is correspondingly symbolised by is Q

_{o}and Q

_{d}. The modelling logic of iceberg-type transport costs involves that only a fraction of the good shipped from o reaches its destination at d, that is, a part of the agricultural good ‘melts away’ in transit. The melting speed is supposed to be a linear function of the geographic distance between locations as in [1]. Thus, the iceberg transport technology for the agricultural good shipped from o to d is given by Equation (1):

_{d}), in relative terms, corresponds to Equation (2):

#### 2.2. Empirical Specification

## 3. Exploratory Spatial Flow Data Analysis

#### 3.1. Agricultural Transport Costs in Peru

**a**) in Table 1, or the other way around, as (

**b**) in Table 1, where n is the number of regions.

_{ij}is the cost of transporting agricultural goods from the origin region i to the destination region j, as approximated in Equation (8) where the values of the main diagonal are the transport costs of agricultural products traded within each region (intraregional flows). (

**a**) in Table 1, each column presents the values of the variable τ

_{iD}corresponding to the transport costs from each of the origin regions i to a specific destination region, D, whereas (

**b**) in Table 1, variables τ

_{Oj}show the transport costs from a given origin region, O, to each of the destination regions j.

#### 3.2. ESFDA of Agricultural Transport Costs

#### 3.2.1. Moran’s I Test of Global Spatial Autocorrelation of Flows

_{ID}of agricultural transport costs, which serves to detect the existence of a linear relationship between the transport cost values of each origin region, i, that carries agricultural goods to a given destination region, D, and the mean values of this variable in the regions neighbouring each origin region, ${\overline{\mathsf{\tau}}}_{iD}$. This statistic I test of destinations (I

_{D}) is expressed as follows:

_{D}statistics as destination regions.

_{Oj}of transport cost from a given origin region to all destination regions. This test serves to detect the existence of a linear relationship between the transport cost values of a given origin region that distributes agricultural products to the rest of the destination regions and the mean value of this variable in the regions neighbouring each destination region. This statistic is called I test of origins (I

_{O}) and is represented as follows:

_{O}statistics as origin regions.

#### 3.2.2. Moran Scatterplots of Spatial Flows

#### 3.2.3. LISA Tests of Local Spatial Autocorrelation of Flows

_{ID}of agricultural transport costs from each origin region i to a specific destination D, which serves to detect the existence of clusters or spatial agglomerations in the vicinity of the origin regions that carry agricultural goods to a certain destination region. This statistic is called I

_{iD}test of destinations:

_{Oj}of agricultural transport cost from a given origin region O to all destination regions j. This test serves to detect the existence of clusters or spatial agglomerations in the vicinity of the destination regions that carry agricultural goods to a certain origin region. This statistic is called I

_{Oj}test of origins:

^{2}dyadic elements of Table 1, for $N=n\times n$ regions.

## 4. Econometric Modelling

#### 4.1. Non-Spatial Origin-Destination Model

_{0}representing a constant parameter term; ${X}_{o}{\beta}_{o}$ and ${X}_{d}{\beta}_{d}$ are respectively ${X}_{o}={\iota}_{n}\otimes X$ and ${X}_{d}={\iota}_{n}\otimes X$, where X is an n-by-n matrix of the natural log of independent variables for the n regions and $\otimes $ represents a Kronecker product, with ${\beta}_{o}$ and ${\beta}_{d}$ being their related scalar parameters; ${D}_{od}$ is an N by 1 vector of the natural log of distance between each o, d pair of regions with α

_{1}and α

_{2}being the associated scalar parameters, and ε is the N by error term vector which is assumed $\epsilon ~N\left(0,{\sigma}^{2}{I}_{N}\right)$, for ${\sigma}^{2}$ the constant variance of the error term and ${I}_{N}$ an identity matrix of order N.

- Gross value added in each region, which measures regional economic dynamics. Since agricultural trade flows are directly proportional to the economic activity in regional economies, we would expect a positive relationship between these flows and the gross value added.
- Consumer price index variation for agricultural products in each region, which approximates the price-demand relationship of agricultural goods. Prices increment should reduce the demand for goods, and lead to reductions of agricultural trade flows, thus effects associated with change to consumer price index should be negative with respect to trade flows.
- Paved neighbourhood road length in each region measures road transport network efficiency. A better-quality infrastructure should lead to more trade, therefore, we would expect a positive relationship between trade flows and paved neighbourhood road length.

#### 4.2. Spatial Origin-Destination Model

#### 4.2.1. Specification

_{o}, W

_{d}, and W

_{w}, respectively. Hence, the spatial autoregressive (SAR) interaction model of agricultural transport flows is expressed as follows:

_{n}) equal in size to that of the spatial weight matrix to describe spatial connectivity between the n regions [26]. The origin spatial weight matrix (W

_{o}), the destination spatial weight matrix (W

_{d}), and the origin-to-destination spatial weight matrix (W

_{w}), are obtained, respectively, as follows:

#### 4.2.2. Estimation of the SAR Origin-Destination Model

**.**There is a high indication of origin- and origin-to-destination-based spatial dependence. These results confirm the effectiveness of the ESFDA for clusters in origin-regions. The coefficients ${\rho}_{o}$ and ${\rho}_{w}$ were 0.64, and 0.48, respectively, and the 99 percent credible intervals indicate they are different from zero. The destination-based spatial dependence captured by ${\rho}_{d}$ = −0.18 also was significant although proved to be the least influential for detecting spatial dependence patterns. The coefficient for the distance variable was significant and negative (−0.0007) and much closer to zero than the least-squares estimate (−0.0085), as shown in Figure 4. It is a usual result for the estimate on distance to fall in significance when spatially lagged variables are included into a SAR interaction model as distance operates as a proxy for spatial dependence when it is not incorporated [30,31].

## 5. Discussion on the Effect Estimates

#### 5.1. Non-Spatial Origin-Destination Model

#### 5.2. Spatial Origin-Destination Model

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Clusters in destination regions created by origin regions: (

**a**) Origin: Piura; (

**b**) Origin: Cajamarca; (

**c**) Origin: San Martín; (

**d**) Origin: Ica.

**Figure 3.**Clusters in origin regions created by destination regions: (

**a**) Destination: Arequipa; (

**b**) Destination: Ica; (

**c**) Destination: Cajamarca; (

**d**) Destination: Lambayeque.

**Figure 4.**Origin-destination transaction networks for agricultural goods; (

**a**) North network; (

**b**) South-Central network.

**Table 1.**Organisation of the data for the agricultural transport cost matrix: (

**a**) Destination-based flows; (

**b**) Origin-based flows.

D_{1} | D_{2} | D_{n} | O_{1} | O_{2} | … | O_{n} | |||

O_{1} |
τ
_{11} | τ_{12} | … | τ_{1n} | D_{1} | τ_{11} | τ_{21} | … | τ_{n1} |

O_{2} |
τ
_{21} | τ_{22} | … | τ_{2n} | D_{2} | τ_{12} | τ_{22} | … | τ_{n2} |

… | … | … | … | … | … | … | … | … | |

O_{n} | τ_{n1} | τ_{n2} | … | τ_{nn} | D_{n} | τ_{1n} | τ_{2n} | … | τ_{nn} |

(a) | (b) |

Clusters in Origin Regions | Clusters in Destination Regions | ||||||
---|---|---|---|---|---|---|---|

Destination | Origin | Moran I | LISA | Origin | Destination | Moran I | LISA |

Arequipa | 0.272 *** | Cajamarca | 0.184 *** | ||||

Cusco | 0.311 *** | La Libertad | 0.518 *** | ||||

Puno | 0.331 *** | Lambayeque | 0.664 *** | ||||

Tacna | 0.430 ** | San Martín | 0.175 *** | ||||

Cajamarca | 0.224 *** | Ica | 0.164 ** | ||||

Ancash | 0.060 ** | Cusco | 0.163 *** | ||||

La Libertad | 0.258 *** | Junín | 0.192 ** | ||||

Lambayeque | 0.039 ** | Lima | 0.086 ** | ||||

MLC ^{a} | 0.331 ** | ||||||

Ica | 0.103 *** | Piura | 0.122 ** | ||||

Apurímac | 0.152 ** | Cajamarca | 0.013 ** | ||||

Arequipa | 0.605 ** | La Libertad | 0.243 *** | ||||

Cusco | 0.008 ** | ||||||

Huancavelica | 0.233 ** | ||||||

Lambayeque | 0.127 ** | San Martín | 0.129 ** | ||||

Cajamarca | 0.351 *** | Cajamarca | 0.354 ** | ||||

San Martín | 0.168 ** | Lambayeque | 0.182 ** | ||||

Piura | 0.447 ** |

^{a}MLC corresponds to Metropolitan Lima and El Callao.

Variable | Description | Units | Mean | Std | Min | Max |
---|---|---|---|---|---|---|

Dependent variable | ||||||

Agricultural trade flows | Agricultural transport costs between each pair of regions. Authors calculations (see Section 3.2). | Dollar per ton/h | 351,504.6 | 542,531.8 | 732.7 | 3,336,130.4 |

Independent variables | ||||||

Regional economic dynamics | Gross value added in each region. National Institute of Statistics and Informatics (INEI) | (Index 2007 = 100) | 137.3 | 20.6 | 89.0 | 189.8 |

Price-demand relationships | Consumer price index variation for agricultural goods in each region. INEI. | Consumer Price Index | 2.8 | 1.3 | 0.4 | 5.7 |

Road transport network efficiency | Paved neighbourhood roads length in each region. Ministry of Transport and Communications (MTC). | km | 77.6 | 94.1 | 66.2 | 403.3 |

Spatial variable | Distance between each pair of regions. Authors calculations based on data from INEI. | km | 720.1 | 413.7 | 56.1 | 1948.9 |

Variable | Least-Squares Model | Spatial Autoregressive | |
---|---|---|---|

Coefficient | Coefficient | ||

Constant | −13.5381 * | −8.6443 | |

β_{d} | consumer price index for agricultural goods | −0.6002 ** | −0.2285 |

β_{d} | paved neighbourhood roads | 0.6885 *** | 0.3143 *** |

β_{d} | regional gross value added | 3.5698 *** | 1.4912 |

β_{o} | consumer price index for agricultural goods | −0.3295 | 0.0579 |

β_{o} | paved neighbourhood roads | 0.1188 | 0.0653 |

β_{o} | regional gross value added | 0.0008 | 0.1286 |

log(distance) | −0.0085 *** | −0.0007 | |

log(distance2) | 0.30 × 10^{−5} *** | 0.13 × 10^{−6} | |

ρ_{d} | −0.1817 * | ||

ρ_{o} | 0.6435 *** | ||

ρ_{w} | 0.4874 *** |

Variables | Least-Squares Model | Spatial Autoregressive | ||||
---|---|---|---|---|---|---|

Mean | Median | Std. Dev. | Mean | Median | Std. Dev. | |

Origin-consumer price index for agricultural goods | 0.0637 | 0.0614 | 0.3079 | −0.1532 | −0.1316 | 1.0399 |

Origin-paved neighbourhood roads | 0.0595 | 0.0596 | 0.0956 | 0.5969 | 0.4749 | 0.7727 |

Origin-regional gross value added | 0.1681 | 0.1422 | 1.0593 | 2.5751 | 2.0815 | 5.1307 |

Destination-consumer price index for agricultural goods | −0.2081 | −0.2102 | 0.3007 | -0.5848 | −0.5369 | 1.1752 |

Destination-paved neighbourhood roads | 0.2967 | 0.2960 | 0.1036 | 1.0031 | 0.8885 | 0.8138 |

Destination-regional gross value added | 1.4238 | 1.4327 | 1.0543 | 4.6975 | 4.1212 | 5.5379 |

Intraregional-consumer price index for agricultural goods | −0.0060 | −0.0060 | 0.0180 | −0.0207 | −0.0186 | 0.0564 |

Intraregional-paved neighbourhood roads | 0.0148 | 0.0149 | 0.0059 | 0.0453 | 0.0409 | 0.0352 |

Intraregional-regional gross value added | 0.0663 | 0.0661 | 0.0628 | 0.2052 | 0.1807 | 0.2516 |

Network-consumer price index for agricultural goods | -- | -- | -- | −5.7770 | −4.0858 | 19.0636 |

Network-paved neighbourhood roads | -- | -- | -- | 12.3269 | 9.3101 | 17.7252 |

Network-regional gross value added | -- | -- | -- | 56.3468 | 38.4989 | 109.0265 |

Total-consumer price index for agricultural goods | −0.1504 | −0.1511 | 0.4493 | −6.5357 | −4.7502 | 21.1928 |

Total-paved neighbourhood roads | 0.3711 | 0.3721 | 0.1471 | 13.9721 | 10.7266 | 19.3182 |

Total-regional gross value added | 1.6582 | 1.6515 | 1.5710 | 63.8246 | 44.3224 | 119.5158 |

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**MDPI and ACS Style**

Herrera-Catalán, P.; Chasco, C.; Torero, M.
Spatial Spillover Effects of Agricultural Transport Costs in Peru. *Land* **2022**, *11*, 58.
https://doi.org/10.3390/land11010058

**AMA Style**

Herrera-Catalán P, Chasco C, Torero M.
Spatial Spillover Effects of Agricultural Transport Costs in Peru. *Land*. 2022; 11(1):58.
https://doi.org/10.3390/land11010058

**Chicago/Turabian Style**

Herrera-Catalán, Pedro, Coro Chasco, and Máximo Torero.
2022. "Spatial Spillover Effects of Agricultural Transport Costs in Peru" *Land* 11, no. 1: 58.
https://doi.org/10.3390/land11010058