1. Ghent University, Belgium
Land productivity and plot size: Is measurement error driving the inverse relationship?
Sam Desiere
Ghent University, Belgium
&
Dean Jolliffe
World Bank, IZA and NPC
Slides prepared for the Land and Poverty Conference 2018: Land Governance in an Interconnected World, Washington, DC: 2018

2. Outline Background – why this matters
Understanding land productivity is central to improving wellbeing of the poor
Extensive empirical history on the inverse relationship between productivity & land size (IR)
Data and methodology
Yield = output / cultivated land size
Focus on output measure
Compare crop cuts with self reports of crop yields
Results
Systematic measurement error in self reports => IR
Implications 1
Introduction
Data & methods
Results
Implications
Conclusion

3. Wellbeing & land productivity
40% of global extreme poverty in sub-Saharan Africa
Ferreira et al (2016)
Large majority of these people are engaged in activities linked to farm land
Livingston et al (2001)
In rest of the world, the vast majority of those living in extreme poor are in rural areas
Povcalnet
10% increase in land productivity estimated to reduce poverty by 7%
Irz et al (2001), Africa 1
Introduction
Data & methods
Results
Implications

4. The inverse relationship between yields and land size (IR)
Yields are declining in farm size
Decades of empirical studies
=> fragmentation improves productivity
=> Suggests no tradeoff between equity and efficiency in terms of land redistribution
Yields are declining in plot size (within a farm)
Accepted as stylized fact in developing countries
=> Farm household irrationally applying labor and other inputs inefficiently
Yields
Cultivated land area 2
Introduction
Data & methods
Results
Implications
Conclusion

5. IR, some candidate explanations:
Missing markets – land, labor, credit, inputs
labor markets (can’t hire in/out) => nonseparable production and consumption decisions, household size determines labor inputs => can explain IR for farm size, but not plot size.
Soil quality
Barret (2010) evidence against soil quality as explanation, marginally linked to IR
Measurement error in land size
Carletto et al. provides some evidence supporting this, but also evidence from at least one country contradicting 3
Introduction
Data & methods
Results
Implications
Conclusion

6. IR, a new explanation: systematic error in self-reports of production
Most/all studies about the IR estimate yields by dividing self-reported production by plot size
Self-reported production is measured with error, and the error can be systematically correlated with plot size
If farmers over report production on small plots and under report it on larger plots, the IR is an artifact of the measurement 4
Introduction
Data & methods
Results
Implications
Conclusion

7. Alternate measure of yield allows us to test this: crop cuts
Crop cuts viewed as a gold standard for measuring yield
Crop cut methodology
Stages 1 & 2: randomly select EA, randomly select plots
Stage 3: randomly select subplot (2m x 2m or 4m x 4m)
Subplot is harvested and weighed (both wet and dry) during harvest by a trained enumerator
Caveat: Crop cuts also measure yield with error
Maximum yield, ignores crop loss
Sampling error (random sub plot selected from plot)
Instrument precision error
Variation in ‘dryness’
BUT we argue there is no reason for the expectation of this error to be correlated with plot size. This is a key assumption. 5
Introduction
Data & methods
Results
Implications
Conclusion

8. Data ESS1 and ESS2 are pooled for power
This also allows us to check temporal external validity
Crop cuts are implemented on a subsample of plots during harvest for 23 crops
2m x 2m subplot in wave 1
4m x 4m subplot in wave 2
Self-reported production reported by plot during third visit (January- March) and plot size measured with GPS
Average recall period for self reports is 85 days
5248 plots with both crop cuts and self-reported production 6
Introduction
Data & methods
Results
Implications
Conclusion

9. Descriptive statistics: maize yields
Median maize yields (kg/ha) by plot size and measurement method (wave 2 only)
1. The IR disappears if yields are based on crop cuts (blue)
2. Yields based on self-reported production (red) are systematically over estimated on small plots
Similar finding for different crops, for wave 1, for means. Also similar finding if we control for household characteristics, labor intensity, EA attributes as seen in regression analysis. 7
Introduction
Data & methods
Results
Implications
Conclusion

10. Methodology, generalizing the descriptive findings
1. Does the IR disappear if yields are measured with crop cuts?
log⁡(𝑦𝑖𝑒𝑙𝑑 𝑖𝑗 )=α log 𝐴 𝑖𝑗 +𝛿 𝑋 𝑖𝑗 +𝛽 𝐿 𝑖 +𝑢 𝑟 +𝜀 𝑖𝑗
Estimate separately for yield measures (crop cut & self-reports), compare α where A is plot size;
X: plot and household characteristics (controlling for possibly nonrandom allocation of plots);
L: labor (controlling for possibly nonrandom effort level by plot size);
𝑢 𝑟 : enumeration area fixed effects (controlling for possibility that EA is correlated with plot size and yield – eg. Soil, hilliness, rainfall) 8
Introduction
Data & methods
Results
Implications
Conclusion

11. Self-reported measurement
Regression Results
The IR is strong if yields are measured with self-reported production,
but disappears if yields are measured with crop cuts
Self-reported measurement
 Crop cuts
(1)
(2)
(3)
(4)
(5)
(6)
Log plot size (m²)
-0.397***
-0.396***
-0.303***
-0.161***
0.104***
0.149***
(-33.26)
(-36.11)
(-12.65)
(-6.22)
(8.63)
(9.36)
Household fixed effects X
Enumeration area fixed effects
Household characteristics
Labor input
Observations
25811
25004
5248
5059
R-squared
0.194
0.201
0.110
0.215
0.120
0.140
Notes: ***, **, * denote statistical significance at the 1%, 5% and 10% levels. T-statistics in parentheses. Errors clustered at the enumeration area. Full results are provided in the appendix. All regressions include a dummy for the wave and plot characteristics.

12. Self-reported production
Regression Results
The IR is strong if yields are measured with self-reported production,
but disappears if yields are measured with crop cuts
Self-reported production
Crop cuts
Log of plot size
-0.303***
-0.161***
0.104***
0.149***
Family labor during harvest
0.292***
0.0591***
Observations
5248
5059 R²
11%
22%
12%
14%
Regressions include plot and household characteristics and enumeration area fixed effects.
***,**,* denote statistical significance at 1%, 5% and 10% 9
Introduction
Data & methods
Results
Implications
Conclusion

13. Core set (sensitivity to extreme values)
Robustness checks
The findings hold in different subsamples
Wave 1
Wave 2
Maize
Core set (sensitivity to extreme values)
Self-reported
Crop cuts
Self-
reported
Crop
cuts
Log of plot size
-0.16***
0.17***
-0.13***
0.14***
-0.44***
0.06
-0.10***
0.11***
Observations
1860
3152
722
4664
4557 R²
20%
10%
25%
36%
18%
17%
13%
Regressions include plot and household characteristics, labor, and enumeration area fixed effects.
***,**,* denote statistical significance at 1%, 5% and 10%
The core set discards bottom and top 5% of yields, 10
Introduction
Data & methods
Results
Implications
Conclusion

14. Supplemental regression analysis, supporting evidence of correlated reporting error and plot size
Are yields based on self-reported production systematically over estimated on small plots relative to crop cuts?
log( 𝑆𝑒𝑙𝑓−𝑟𝑒𝑝𝑜𝑟𝑡𝑒𝑑 𝑦𝑖𝑒𝑙 𝑑 𝑖 𝐶𝑟𝑜𝑝−𝑐𝑢𝑡 𝑦𝑖𝑒𝑙𝑑 𝑖 )=α log 𝐴 𝑖 +𝛿 𝑋 𝑖 +𝛽 𝐿 𝑖 +𝑢 𝑟 +𝜀 𝑖
Estimate separately for yield measures (crop cut & self-reports), compare α where A is plot size;
X: plot and household characteristics (controlling for possibly nonrandom allocation of plots);
L: labor (controlling for possibly nonrandom effort level by plot size);
𝑢 𝑟 : enumeration area fixed effects (controlling for possibility that EA is correlated with plot size and yield – eg. Soil, hilliness, rainfall) 8
Introduction
Data & methods
Results
Implications
Conclusion

15. Results, supplemental evidence on systematic measurement error in self-reported production
Assuming self-reports over estimate true production (as suggested by existing empirical literature), a decline in the value of the ratio of yields indicates a decline in the measurement error in self reports.
=>
The regression results provide support to the suggestion that measurement error in self reports is declining in plot size.
Estimation of systematic measurement error in self-reported production
Dependent variable: Ratio of self-report over crop-cut yields
Log of plot size
-0.295***
-0.287***
Family labor during harvest
0.226***
Observations
5914
5053
Regressions include plot and household characteristics and enumeration area fixed effects.
***,**,* denote statistical significance at 1%, 5% and 10% 11
Introduction
Data & methods
Results
Implications
Conclusion

16. ME in self report explains IR in ET, Is the finding valid for other countries?
1. Findings hold across crops and waves
2. ESS data is representative of the rural population in Ethiopia
Our analysis is based on a random subsample of the ESS – A household is in our sample if one of their plots was randomly selected for crop cuts
Subsample with crop cuts looks similar to rest of population (except for landholdings, which is to be expected since household with more plots more likely to be in sample)
No crop cuts
Crop cuts
difference (t-value)
Landholdings (ha)
1.18
1.34
3.07
***
Applied chemical fertilizer (%) 47 50
1.29
Asset index
0.16
0.17
2.00 **
Household size
5.75
5.90
1.62
Age household head
46.47
45.67
1.42
Household head can read & write (%) 38 39
0.73
Female headed household (%) 20 17
1.50
N (min/max)
2954/3018
878/890
Notes: Number of observations differs by variable due to missing variables. T-values estimated by clustering
the standard errors at the enumeration area. ***, **, * denote statistical significance at the 1%, 5% and 10% levels.

17. Implications for the IR
Rejection of a negative correlation between plot size and land productivity implies that:
Rejecting plot-level IR aligns with conventional wisdom that fragmentation increases (not reduces) inefficiencies.
Also refutes inference that farmers behave irrationally in allocation of inputs across plots
With no IR at plot level, missing markets may explain the inverse productivity farm-size relationship
Any regression with farm output as a regressor, needs to be attentive to bias induced by the correlated measurement error (output and anything related to plot size). 12
Introduction
Data & methods
Results
Implications
Conclusion

18. Systematic measurement error and dynamics, one example
Systematic measurement error can invalidate time trends
Example: strong population growth -> smaller plots per capita -> production is over reported on smaller plots -> yields increase
Statistician concludes: population growth -> increases yields (i.e Boserup is right, Malthus is wrong) But this conclusion is false here 14
Introduction
Data & methods
Results
Implications
Conclusion

19. Conclusion
Measurement error in self-reported production is the primary causal source of the inverse-relationship between productivity and plot size.
Our estimates suggest that production is over-stated by 40% to 100% for plots of 100m², and under-stated by 10% to 35% on plots of 3000m² in the case of rural Ethiopian households
Rejecting IR at plot level resurrects missing-market explanations for IR and farm-size level.
Of course, more research is needed to establish whether this is the explanation for plot-level IR is unique to Ethiopia (or countries ‘like’ Ethiopia, in some relevant dimension). 15
Introduction
Data & methods
Results
Implications
Conclusion

20. Acknowledgments & Data
Ethiopia Socioeconomic Survey (ESS) data was collected in collaboration with Ethiopia’s Central Statistical Agency
This research was generously funded by UK’s Department for International Development – Ethiopia Office
ESS publicly available: go.wordlbank.org/ZK2ZDZYDD0
ESS3 (third wave) coming soon

21. Implications beyond the IR
A. Random error reduces the precision
B. Systematic error implies a bias between the ‘true’ value and the outcome of the measurement
Bias is constant
Bias correlates with observable and unobservable characteristics
Systematic error correlated with important (household) characteristics is the nightmare of every statistician 13
Introduction
Data & methods
Results
Implications
Conclusion

22. (Disturbing) implications of the IR
Land redistribution improves equality and efficiency
Policymakers should focus on small-scale farmers (rather than large-scale agriculture) to improve ag productivity
Land consolidation will not increase total agricultural production
Farmers behave irrationally since they do not allocate labor and inputs efficiently across plots
Because of the important policy implications, an extensive theoretical and empirical literature about the IR has emerged 3
Introduction
Data & methods
Results
Implications
Conclusion

23. Analysis based on ESS, publicly available at:
Desiere, S., Jolliffe, D., “Land productivity and plot size: Is measurement error driving the inverse relationship?” Journal of Development Economics 130, 84–98. doi.org/ /j.jdeveco
Analysis based on ESS, publicly available at: