6 Responses to A behavioral solution to the inverse size-productivity puzzle?

  1. duncan boughton says:

    Great work Leah. A question? Why would you not expect biophysical effects at the edges of plots? Surely the plants on the edges have less competition for light, water and nutrients from other plants on the inside. Also, if the plot is demarcated by a bund, they may even get extra moisture and nutrients from run in.
    The finding that the effects are at the plot level rather than the household level also makes me wonder whether edge effects alone can explain the higher productivity of small plots in the aggregate. Wouldn’t the higher productivity at the edge be at least partially offset by the unutilized land making up the plot boundary? If you control for the unplanted boundary do you still get higher productivity from small plots?
    I think part of the reason we find it difficult to come up with consistent results on small plot productivity at the household level, at least where food staples are concerned, is the opportunity price (consumption value) of marginal output. If the household cannot rely on staple food markets, either because of market failure or lack of purchasing power, then they will want to maximize output per unit area where land is constraining. But if they have other options, resulting in a lower opportunity price for own consumption, they may choose a lower level of productivity even when land area is constrained.
    Thanks for chipping away at the edges of this puzzle and all the best at Ohio State!

    • Hi Duncan, thanks for your comments! Let me elaborate a tiny bit.

      We absolutely do expect biophysical effects at plot edges… sunlight, nutrient availability, soil moisture, and soil/crop biodiversity may all change around plot edges, and agronomists have cited these as potential reasons for increased productivity around plot peripheries. We discuss this in the paper, but unfortunately we can’t directly test for these mechanisms, because we don’t observe the biophysical inputs. We actually do conduct a series of indirect tests (e.g., is the edge effect stronger for plots with taller plants, where sunlight is more likely to be blocked in the interior?), and find no evidence for biophysical mechanisms… but at the end of the day, we don’t really know. So we throw these indirect tests in an appendix, as they certainly can’t rule out biophysical mechanisms, but they also don’t support them. We CAN test for the behavioral mechanism, because we observe labor at the plot level, and so we focus on this largely because it’s feasible. (Oh, and we don’t observe whether a boundary is planted or not, though I wish we did.)

      So, to be clear on farm vs. plot: we DO find the inverse relationship at the farm level, for sure. But once we control for plot size, the importance of farm size completely disappears. So in our data, the inverse farm size-productivity ratio is completely explained by the inverse plot size-productivity ratio. Barrett, Bellemare and Hou (2010) find something similar — in their data from Madagascar, the plot-level relationship is lessened slightly by household fixed effects but remains strongly negative and significant. In our data, the plot-level inverse relationship actually becomes stronger with household fixed effects. Carletto, Savastano and Zezza (2013) also estimate a plot-level relationship… so while external validity is of course an issue, I personally have a hunch that in most cases it’s really the plot-level relationship driving the farm-level relationship. But maybe not.

      I totally agree that knowing how to price/value crops for smallholders is hugely difficult, for the reasons you mention among others. I like it, personally, when people present productivity results using both kg and value as a metric… which we actually don’t include in the current version of our paper. But I have the results myself, and the plot-level inverse relationship can be estimated with production in kg or value.

      Thanks so much for your thoughts!

  2. Rebel Good says:

    How do you control for shape of the plot? Does the “spaghetti” farmer have higher productivity than from a comparable-in-area plot that is circular?
    I really don’t know what I’m talking about, but I’m Chris Barrett’s brother, so I thought I’d ask.

    • Thanks for the question!

      Your intuition is exactly right… long, thin plots with most/all of their area around at the edge of the plot will be more productive than circular or square plots with a lot of interior space.

      We don’t control directly for the shape of the plot (i.e., triangle vs. square vs. circle), but we capture how much of the plot is at the “edge” by controlling for (Perimeter/Total Plot Area). Controlling for that ratio doesn’t *perfectly* capture (Peripheral Area/Total Area), but it does pretty well. You can see why if you look at Equations 6-9 in the linked working paper — I skipped the math for the blog.

      We are able to calculate perimeter because we have GPS waypoints at all the vertices of the plot. A lot of surveys these days take these waypoints, but only calculate plot area with them… I think keeping the waypoints themselves is always a good policy though, as both shape and perimeter may play into plot management in ways that economists often ignore.


  3. John Gershman says:

    Very nice paper and work. Another possible thought on the edge effect, although one not easily measured. Is there some kind of property rights effect in which working on the plot edges serves as a form of de facto “patrolling” of property rights in situations where fences or other forms of boundary markers are not common and/or property rights are less secure?

    • Great thought, thanks!

      I actually just looked into this a couple weeks ago, after Marc Bellemare raised almost exactly the same point. (Great minds…) The idea seems plausible, and I tried estimating the edge effect across various types of land tenure in case “more secure” farmers, as you say, feel less compelled to build up the edges of their plot. I didn’t find significant differences across land tenure types — though our dataset has almost no temporal variation in plot-level tenure, and very little cross-sectional variation either. Pretty much all farmers own their plots (almost no renting, leasing, share-cropping), and the two existing ownership types are not very different, and don’t change much across time.

      I didn’t try estimation according to fencing status, and I’ll do that… but I believe variation will be just as low here. Very few farmers have plot fencing in our dataset.

      Being irritated that I had low tenure variation in our dataset, I actually tried using the Uganda LSMS-ISA dataset to look at something similar… estimating the parcel-level inverse relationship across tenure types. (I don’t have perimeter length for the LSMS-ISA dataset, and so cannot look directly at the edge effect.) While nationally representative, these data still have very little variation in tenure type — and the inverse relationship did not vary much across the categories that do exist. So, I think Uganda is not the best place to investigate this idea.

      Of course, examining tenure or fencing is an indirect test of the hypothesis… it’s possible that all farmers, regardless of their land security, do build up the edge of their plot in part to mark boundaries. In which case, I’m unable to separate that from the other behavioral effect of simply attending the edges due to spatial awareness and/or accessibility.

      Thanks again for the comment! Please feel free to send along any other thoughts, by comment or by email. Note that I’ve added a link to the working draft of the paper, if you wish to skim the whole thing.


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