# Agricultural Land Price Convergence: Evidence from Polish Provinces

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## Abstract

**:**

## 1. Introduction

## 2. Methodology and Data

#### 2.1. Methodology of Testing Agricultural Land Price Convergence

- Construct the cross-sectional variance ratio ${H}_{1}/{H}_{t}$ using the formula:$${H}_{t}=\frac{1}{N}{{\displaystyle \sum}}_{i=1}^{N}{\left({h}_{it}-1\right)}^{2},{h}_{it}=\frac{\mathrm{ln}{p}_{it}}{{N}^{-1}{{\displaystyle \sum}}_{i=1}^{N}\mathrm{ln}{p}_{it}}$$
- Run the log t regression:$$\mathrm{log}\left(\frac{{H}_{1}}{{H}_{t}}\right)-2\mathrm{log}\left(\mathrm{log}\left(t\right)\right)=a+b\mathrm{log}\left(t\right)+{\epsilon}_{t}$$
- Assess the convergence of the entire sample using the t-statistic$.$ If $\widehat{{t}_{b}}<-1.65$, the null hypothesis is rejected, which indicates that land prices across all provinces tend to diverge. There is still the possibility, however, that convergence clubs occur in the data, i.e., the group of provinces where prices share a common trend in the long run.

- Extract the trend component from analysed time series (it is also required at previous stages).
- Order the provinces in the panel in decreasing order according to prices in the last period.
- Form a core group of provinces ($k$) in the panel based on the log t regression maximising ${t}_{k}$ with ${t}_{k}>-1.65$.
- Add to the core group one province and run the log t regression and check if ${t}_{k}>-1.65$ or ${t}_{k}>0$, respectively for large and small $T$. If true, add the new province to the core group.
- For the rest of provinces that do not meet the condition outlined in previous step run the log t regression and check if ${t}_{k}>-1.65$. If true, the second convergence clubs is established. If not, repeat the previous steps to verify if the remaining provinces can be further subdivided.
- Try to merge initial convergence clubs. For example if club 1 and club 2 meet the convergence hypothesis merge the clubs into new club. Next, try to merge the new club with initial club 3. Continue this procedure until no clubs can be merged.

#### 2.2. Methodology of Studying the Driving Forces of Convergence

#### 2.3. Study Area

#### 2.4. Data—Studying the Convergence

#### 2.5. Data—Studying the Driving Forces of the Convergence

## 3. Results and Discussion

#### 3.1. Studying Land Price Convergence

#### 3.2. Studying the Driving Forces of Convergence

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Results of the σ-convergence test in the years 1999–2018. Note: land prices are ln-transformed.

**Figure 4.**(

**a**) Convergence clubs for medium-quality land. (

**b**) Convergence clubs for bad-quality land. Note: estimates using the Hodrick–Prescott filter. Stata and QGis software was used to obtain the estimates.

**Figure 5.**(

**a**) Estimates of transition paths for good-quality land using the Hodrick–Prescott filter. (

**b**) Estimates of transition paths for good-quality land using the Hamilton filter. (

**c**) Estimates of transition paths for medium-quality land using the Hodrick–Prescott filter. (

**d**) Estimates of transition paths for medium-quality land using the Hamilton filter. (

**e**) Estimates of transition paths for bad-quality land using the Hodrick–Prescott filter. (

**f**) Estimates of transition paths for bad-quality land using the Hamilton filter. Notes: there are sixteen transition paths representing all provinces in Poland in each panel above. Convergence exists when all curves tend to narrow toward unity. Stata software was used to obtain the estimates.

Year | Urbanisation (%) | Salary (PLN) | GDP (PLN) | Agricultural Production (PLN) | Pigs (Units) | Agricultural Commodity Price (PLN) | Interest Rate (%) |
---|---|---|---|---|---|---|---|

2001 | 4.63 | 1807.19 | 18,839.63 | 2684.21 | 52.48 | 58.35 | 14.5 |

2002 | 4.69 | 2081.07 | 19,594.13 | 3387.56 | 56.96 | 50.68 | 8.25 |

2003 | 4.83 | 2147.57 | 20,423.81 | 3255.69 | 55.44 | 52.39 | 5.88 |

2004 | 4.82 | 2238.16 | 22,518.13 | 3555.13 | 52.66 | 56.38 | 6.00 |

2005 | 4.90 | 2321.60 | 23,865.00 | 3930.75 | 55.98 | 45.00 | 5.00 |

2006 | 4.96 | 2439.83 | 25,755.63 | 3596.38 | 55.75 | 53.04 | 4.13 |

2007 | 4.96 | 2652.55 | 28,639.88 | 3988.50 | 52.13 | 78.47 | 4.63 |

2008 | 5.03 | 2919.96 | 31,039.63 | 4744.81 | 42.26 | 74.38 | 5.88 |

2009 | 5.09 | 3054.96 | 32,584.88 | 4798.94 | 42.63 | 57.56 | 3.88 |

2010 | 5.15 | 3181.44 | 34,160.06 | 4604.75 | 44.33 | 68.71 | 3.50 |

2011 | 5.23 | 3350.54 | 36,940.19 | 5238.25 | 38.83 | 92.48 | 4.13 |

2012 | 5.30 | 3471.52 | 38,343.88 | 6051.13 | 32.98 | 101.60 | 4.50 |

2013 | 5.38 | 3596.69 | 39,003.44 | 6774.31 | 31.98 | 92.67 | 3.13 |

2014 | 5.44 | 3719.73 | 40,510.19 | 7363.69 | 32.94 | 79.92 | 2.00 |

2015 | 5.51 | 3857.65 | 42,353.94 | 6656.50 | 30.63 | 77.46 | 1.50 |

2016 | 5.59 | 3993.79 | 43,766.81 | 6868.13 | 32.36 | 73.12 | 1.50 |

2017 | 5.66 | 4217.73 | 46,682.06 | 6741.13 | 34.45 | 78.69 | 1.50 |

2018 | 5.71 | 4497.43 | 49,567.56 | 7221.50 | 31.55 | 84.57 | 1.50 |

Type of Land | $\widehat{\mathit{b}}$ (HP Filter) | t-Statistic (HP Filter) | $\widehat{\mathit{b}}$ (HAM Filter) | t-Statistic (HAM Filter) |
---|---|---|---|---|

Good-quality Land | −0.1847 | −1.5752 | 0.4224 | 2.5215 |

Medium-quality Land | −0.2829 ** | −2.5140 | 0.4640 | 3.0044 |

Bad-quality Land | −0.2543 ** | −2.0606 | 0.6404 | 4.3025 |

Type of Land | Club 1 Provinces | $\widehat{\mathit{b}}$ | (t-Statistic) | Club 2 Provinces | $\widehat{\mathit{b}}$ | (t-Statistic) |
---|---|---|---|---|---|---|

Good-quality Land | 16 | −0.1847 | −1.5752 | 0 | NA | NA |

Medium-quality Land | 12 | 0.2259 | 1.7515 | 4 | 1.5659 | 8.7746 |

Bad-quality Land | 11 | 0.5579 | 2.8522 | 5 | 1.3886 | 5.1730 |

Variable | Club 1 | Club 2 |
---|---|---|

Average farm size (ha) | 15.0 | 5.7 |

Labour productivity (PLN) | 70,519.1 | 24,412.9 |

Degree of commodity (%) | 95.6 | 88.8 |

Land productivity per hectare of farmland (PLN) | 7081.4 | 7529.8 |

Type of Land | Hausman | Pesaran | Breusch-Pagan |
---|---|---|---|

Good-quality Land | 75.13 *** | 14.78 *** | 325.02 *** |

Medium-quality Land | 63.66 *** | 13.14 *** | 332.78 *** |

Bad-quality Land | 58.00 *** | 10.96 *** | 282.02 *** |

Variable | Good-Quality Land | Medium-Quality Land | Bad-Quality Land |
---|---|---|---|

$\mathrm{ln}{p}_{i,t-1}$ | 0.8374 *** | 0.9559 *** | 0.9875 *** |

$\mathrm{ln}{p}_{i,t-2}$ | −0.1436 | −0.2501 *** | −0.2756 *** |

Urbanisation | −0.3832 *** (−1.25) | −0.4259 *** (−1.45) | −0.5382 *** (−1.87) |

Salary | −0.2194 (−0.72) | −0.0654 (−0.22) | 0.0835 (0.29) |

Agricultural Production | 0.1482 (0.48) | 0.1237 (0.42) | 0.1152 (0.40) |

GDP | 0.3883 ** (1.27) | 0.3544 * (1.20) | 0.4138 ** (1.44) |

Pigs | −0.0132 (−0.04) | 0.0437 (0.15) | 0.0886 ** (0.31) |

Agricultural Commodity Price | 0.2594 *** (0.85) | 0.2525 ** (0.86) | 0.2065 * (0.72) |

Interest Rate | −0.1417 ** (−0.46) | −0.1139 ** (−0.39) | −0.0820 * (−0.28) |

${R}^{2}$ | 0.9850 | 0.9860 | 0.9844 |

Type of Land | Elasticity in the Long-Run |
---|---|

Good-quality Land | 1.24 *** |

Medium-quality Land | 0.75 *** |

Bad-quality Land | 0.70 *** |

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**MDPI and ACS Style**

Tomal, M.; Gumieniak, A. Agricultural Land Price Convergence: Evidence from Polish Provinces. *Agriculture* **2020**, *10*, 183.
https://doi.org/10.3390/agriculture10050183

**AMA Style**

Tomal M, Gumieniak A. Agricultural Land Price Convergence: Evidence from Polish Provinces. *Agriculture*. 2020; 10(5):183.
https://doi.org/10.3390/agriculture10050183

**Chicago/Turabian Style**

Tomal, Mateusz, and Agata Gumieniak. 2020. "Agricultural Land Price Convergence: Evidence from Polish Provinces" *Agriculture* 10, no. 5: 183.
https://doi.org/10.3390/agriculture10050183