# Structural Changes in Israeli Family Farms: Long-Run Trends in the Farm Size Distribution and the Role of Part-Time Farming

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Institutional Background

## 3. Methodology

^{k}and z

^{k}(x) are defined as:

_{k}) that describes end-period farm size (x

_{1}) as a function of beginning-period farm size (x

_{0}): ${x}_{1}={g}_{k}({x}_{0})$. Using the inverse of g

_{k}, we can express the end-period density as:

_{k}, we can construct specific approximations of the changes in the farm size density. For example, suppose that we choose a linear function:

_{k}= 1. The linear transformation g

_{k}now reflects an additive increase of a constant number of units, α

_{k}, in the size of all farms in subgroup k. In terms of the density function, this is reflected in a horizontal shift of the entire function, which is denoted as sliding. Calibrating to the increase in average farm size, we obtain ${\alpha}_{k}=E({f}_{1}^{k})-E({f}_{0}^{k})$. Using these parameters, (7) is now denoted as ${\varsigma}_{1}^{k}(x;{\mu}_{1}^{k},{\sigma}_{0}^{k})$, where the subscript “0” of the standard deviation means that we keep the spread of the initial period, and the subscript “1” of the mean of the distribution means that the approximated distribution has the same mean as the actual distribution in the final period.

_{k}= s, ${\alpha}_{k}=(1-s)E({f}_{0}^{k})$. It is easy to verify that this transformation does not change the mean of farm size, but increases the standard deviation by a factor of s. Hence, the calibration to the final-period standard deviation requires setting $s=\sqrt{Var({f}_{1}^{k})/Var({f}_{0}^{k})}$. Using these parameters, (7) is now denoted as ${\varsigma}_{1}^{k}(x;{\mu}_{0}^{k},{\sigma}_{1}^{k})$, where the subscript “0” of the mean of the distribution means that we keep the mean of the initial period, and the subscript “1” of the standard deviation means that the approximated distribution has the same standard deviation as the actual distribution in the final period.

_{k}= $s=\sqrt{Var({f}_{1}^{k})/Var({f}_{0}^{k})}$ and ${\alpha}_{k}=E({f}_{1}^{k})-E({f}_{0}^{k})$. The resulting approximated density based on (7) is denoted as ${\varsigma}_{1}^{k}(x;{\mu}_{1}^{k},{\sigma}_{1}^{k})$. We are now in the position to decompose the change in the subgroup density function of farm size into the three components: sliding, stretching and squashing. Note that both sliding and stretching can be obtained in two ways. Sliding, for example, is the change in the mean, but it can be conditioned on the standard deviation of either the initial period or the final period. Similarly, stretching is the change in the standard deviation, but it can be conditioned on the mean of the initial period or the final period. We solve this problem by weighting each of these possibilities in a way that leaves squashing as a residual. The resulting decomposition is:

## 4. Data

## 5. Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Changes in the value added of agricultural production and the number of self-employed farmers (percent).

**Figure 3.**Changes in the income of farmers and the fraction of fruits and vegetables that are exported.

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**MDPI and ACS Style**

Kimhi, A.; Tzur-Ilan, N.
Structural Changes in Israeli Family Farms: Long-Run Trends in the Farm Size Distribution and the Role of Part-Time Farming. *Agriculture* **2021**, *11*, 518.
https://doi.org/10.3390/agriculture11060518

**AMA Style**

Kimhi A, Tzur-Ilan N.
Structural Changes in Israeli Family Farms: Long-Run Trends in the Farm Size Distribution and the Role of Part-Time Farming. *Agriculture*. 2021; 11(6):518.
https://doi.org/10.3390/agriculture11060518

**Chicago/Turabian Style**

Kimhi, Ayal, and Nitzan Tzur-Ilan.
2021. "Structural Changes in Israeli Family Farms: Long-Run Trends in the Farm Size Distribution and the Role of Part-Time Farming" *Agriculture* 11, no. 6: 518.
https://doi.org/10.3390/agriculture11060518