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On the growth process of US agricultural land

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Abstract

In this article, we show that the growth process of US county-level farmland is remarkably consistent with the Gibrat’s law of proportionate effect, an empirical regularity frequently observed across various disciplines. This implies farmland grows proportionately over time (farmlands, whether large or small, on average grow at similar rates) and that there is little empirical support for the presence of diseconomies of size for US farmland. Granted that a random multiplicative growth is the prevalent attribute of models explaining the genesis of power laws, confirmation of Gibrat’s law also offers a possible explanation for the emergence of a power law in the distribution of US county-level farmland size.

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Notes

  1. Bunge (2017) provides an excellent review of the history of farm consolidation in the USA.

  2. Adamopoulos and Restuccia (2014) show that the improved productivity and efficiency of larger farms are a result that holds even after accounting for differences in land scarcity, soil, geography, agrarian structure, and form of agriculture.

  3. For a modern interpretation of the Gibrat’s law, and a review of Gibrat’s work in general, see Akhundjanov and Toda (2020).

  4. For an in-depth discussion, see Shapiro et al. (1987) and Clark et al. (1992).

  5. For instance, for the state of California, which is the leading agricultural state in the USA, see state agricultural production statistics at https://www.cdfa.ca.gov/Statistics/, all of which are reported at the county level, and individual county agricultural reports at https://www.cdfa.ca.gov/exec/county/CountyCropReports.html.

  6. A concern that may arise with estimating Eq. (6)—and variations of it—using an OLS is the potential endogeneity bias stemming from the lagged farmland, \(S_{t-1}\), on the right-hand side of the equation. One could argue that the lag of size is in part explained by previous shocks of growth, and hence, it is not entirely exogenously determined. This issue, however, has been broadly ignored in empirical applications of Gibrat’s law, including in the seminal work (see, for instance, Eeckhout 2004). This is partly due to the fact that models of random growth, such as that embodied in equation (6), are at the core of Gibrat’s law (Sutton 1997; Gabaix 1999). Besides, as noted by Duranton and Puga (2014), studying growth processes at sub-unit levels (e.g., cities and counties) within a country is easier and simpler than growth of entire countries because large cross-country growth regressions are afflicted by heterogeneity and endogeneity problems that are much less important in the context of sub-units (e.g., cities and counties) within a country. The methodology, as well as the unit of analysis, adopted in our study appear largely plausible in light of these studies.

  7. A slight difference in the significance of coefficients of interest (\(\beta \)’s) in panels B and D of Table 2 may be attributed to the dynamics in farm consolidation in the USA. As reported by MacDonald et al. (2018), the pace of farm and cropland consolidation slowed around 2007. This means before 2007, when the consolidation was still rapid, the distribution of US agricultural land was not entirely polarized, and this may likely explain a very weak (1.408\(\times 10^{-8}\) and 1.191\(\times 10^{-8}\), to be precise) dependence between growth and size for 1997-2002 in panels B and D of Table 2.

  8. Interestingly, Clark et al. (1992) showed, using extensive Monte Carlo simulations, that if Gibrat’s law is not rejected in the aggregate data, then there is a strong likelihood that it will not be rejected in the component (farm-level) data.

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Authors and Affiliations

  1. Department of Applied Economics, Utah State University, 4835 Old Main Hill, Logan, Utah, 84322-4835, USA

    Sherzod B. Akhundjanov

  2. Department of Applied Economics, Utah State University, Logan, USA

    Tatiana Drugova

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  1. Sherzod B. Akhundjanov
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  2. Tatiana Drugova
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Correspondence to Sherzod B. Akhundjanov.

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The authors are grateful to two anonymous reviewers as well as participants at the Agricultural and Applied Economics Association (2020) meeting for their helpful comments and suggestions. This research was supported in part by the USDA-NIFA-AFRI Markets and Trade Priority Area of the Agriculture Economics and Rural Communities (AERC) Program under award 2020-67023-30962 and the Utah Agricultural Experiment Station (UAES). All remaining errors are our own.

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Akhundjanov, S.B., Drugova, T. On the growth process of US agricultural land. Empir Econ 63, 1727–1740 (2022). https://doi.org/10.1007/s00181-021-02180-7

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