metadata: authors: 0: author: Carletto,Calogero
1: author: Savastano,Sara
2: author: Zezza,Alberto
count: Uganda,Africa
docna: 0: docna: Fact or artefact : the impact of measurement
            errors on the farm size - productivity relationship
docty: Policy Research Working Paper
theme: Other environment and natural resources management,Rural non-farm income generation,Other human development,Nutrition and food security,Rural services and infrastructure
majtheme: Environment and natural resource management,Human development,Rural development
subtopic: Food Security,Educational Sciences,Crops and Crop Management Systems,Climate Change and Agriculture,Labor & Employment Law,Labor Markets,Rural Labor Markets
teratopic: Education,Agriculture,Law and Development,Social Protections and Labor,Rural Development
abstracts: cdata!: This paper revisits the role of land
            measurement error in the inverse farm size and productivity
            relationship. By making use of data from a nationally
            representative household survey from Uganda, in which
            self-reported land size information is complemented by plot
            measurements collected using Global Position System devices,
            the authors reject the hypothesis that the inverse
            relationship may just be a statistical artifact linked to
            problems with land measurement error. In particular, the
            paper explores: (i) the determinants of the bias in land
            measurement, (ii) how this bias varies systematically with
            plot size and landholding, and (iii) the extent to which
            land measurement error affects the relative advantage of
            smallholders implied by the inverse relationship. The
            findings indicate that using an improved measure of land
            size strengthens the evidence in support of the existence of
            the inverse relationship.
repnme: repnme: Fact or artefact : the impact of
            measurement errors on the farm size - productivity relationship
display_title: Fact or artefact : the impact of
            measurement errors on the farm size - productivity relationship
listing_relative_url: /research/2011/12/15545065/fact-or-artefact-impact-measurement-errors-farm-size-productivity-relationship
topicv3: Agriculture and Food Security m1326205 435,Labor Markets m1326488 855,Crop Production m1326627 174,Education m1327048 470,Household Surveys m1504071 2761
publishtoextweb_dt: 2011-11-30T00:00:00Z
historic_topic: Education,Agriculture,Law and Development,Social Protections and Labor,Rural Development
no_of_pages: 24
author_keys: 0: author_key: 550790
1: author_key: 435265
2: author_key: 635976
model_extractions: WPS5908 Policy Research Working Paper 5908

# Fact or Artefact

The Impact of Measurement Errors on the Farm Size - Productivity Relationship _Calogero Carletto Sara Savastano Alberto Zezza_ The World Bank Development Research Group Poverty and Inequality Team December 2011
Policy Research Working Paper 5908

# **Abstract**

This paper revisits the role of land measurement error in the inverse farm size and productivity relationship. By making use of data from a nationally representative household survey from Uganda, in which self-reported land size information is complemented by plot measurements collected using Global Position System devices, the authors reject the hypothesis that the inverse relationship may just be a statistical artifact linked to problems with land measurement error. In particular, the paper explores: (i) the determinants of the bias in land measurement, (ii) how this bias varies systematically with plot size and landholding, and (iii) the extent to which land measurement error affects the relative advantage of smallholders implied by the inverse relationship. The findings indicate that using an improved measure of land size strengthens the evidence in support of the existence of the inverse relationship.

This paper is a product of the Poverty and Inequality Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at gcarletto@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Fact or Artefact: The Impact of Measurement Errors on the Farm Size - Productivity Relationship**<sup>**1**</sup>

Calogero Carletto<sup>2</sup> Sara Savastano Alberto Zezza

**Keywords: Inverse Farm Size Productivity Relationship, Land Measurement Error, Uganda,**

**JEL Classification: O13, Q12, C81,**

Corresponding Author: Gero Carletto The World Bank 1818 H St. NW Washington DC, 20433 Email: gcarletto@worldbank.org

> 1 The views expressed in this paper are the authors‟ only and should not be attributed to the institutions they are affiliated with. The authors are grateful to Hans Binswanger, Keijiro Otsuka, Franco Peracchi, Christopher Udry, Paul Winters, and participants in the ICAS-V Conference in Kampala, Uganda (October 2010) for their comments on an early version of this work.

> 2 Calogero Carletto and Alberto Zezza are with the Development Research Group of the World Bank.  Sara Savastano is with the University of Rome, Tor Vergata.

1
# **1. Introduction**

The controversy over the existence of an inverse relationship between farm size and productivity (IR henceforth) is one of the longest standing and more ideologically charged pieces of the agricultural development literature. Should smallholders be found to be more efficient, policies to facilitate the redistribution of land towards small famers may be justified not only on equity but also on efficiency grounds. Binswanger et al. (1995) and Eastwood et al. (2010) provide comprehensive reviews of the arguments and a historical account of the empirical evidence on the IR. In the context of African agriculture, the relationship has been most recently questioned by Collier and Dercon (2009) who maintain that “there are (only) a handful of reasonably careful studies showing the inverse farm-size/productivity relationship in African settings, but also some showing the reverse (i.e. positive) farm-size/productivity relationship”.

A substantial part of the debate, particularly in recent years, has focused on whether the IR may be a statistical artifact, stemming from problems with the available data. The possible role of the omission or imprecise measurement of land quality traits in determining the empirical findings on the IR has been examined by several authors (Walker and Ryan, 1990; Binswanger et al., 1995; Benjamin, 1995; Bhalla and Roy, 1998; Lamb, 2003). Barrett et al. (2010) have probably put an end to that aspect of the controversy convincingly using laboratory tests on soil samples to show that only a minimal part of the IR can be explained by differences in land quality. We are aware of only one study (Lamb, 2003) that attempts to empirically test the robustness of the IR to possible errors in land area measurement. The conclusion of that study, which controls for errors in land measures indirectly by comparing fixed and random effect estimates, is that when errors in self-reported farm size are accounted for the IR can be completely explained by factor market imperfections and differences in land quality.

In this paper, we revisit the role of land measurement error in the IR controversy by drawing on data from a nationally representative household survey from Uganda, in which self-reported land size information were complemented by plot measurements collected using Global Position System (GPS) devices. This allows us to systematically analyze the differences in land area data using both measurements, and discuss the impact of such differences on estimates of agricultural productivity. In particular, we explore: (i) what are the determinants of the bias in land measurement, (ii) whether this bias varies systematically with plot size and landholding, and (iii) whether the data support the IR hypothesis, and the extent to which land measurement error affects the relative advantage of smallholders implied by the IR. Preliminary empirical evidence (Goldstein and Udry, 1999) suggests that the differences between GPS and self-reporting may be substantial, and that such difference varies by farm size. If this intuition is correct, using GPS data can have considerable implications for the much debated and contentious relationship between farm size and productivity.

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The paper is organized as follows. The next section succinctly reviews the main strands of literature this paper relates to. Section 3 provides a description of the data. The econometric models used are sketched in Section 4 and the results discussed in Section 5. The final section summarizes the contributions of the analysis to the literature and to the policy discussion around smallholders‟ productivity.

# **2. The inverse farm size-productivity relationship: Smallholder advantage or statistical artefact?**

Starting with the seminal work of Sen (1962, 1966) who observed an inverse relationship between farm size and output per hectare in Indian agriculture, a large number of empirical studies have presented evidence that appears to corroborate that hypothesis (Barrett, 1996; Carter, 1984, Eswaran and Kotwal, 1985, 1986; Lau and Yotopoulos, 1971; Benjamin and Brandt, 2002; Berry and Cline, 1979). A smaller set of empirical studies however does not find evidence of such a relationship (Hill, 1972, Kevane, 1996, Zaibet and Dunn, 1998). Binswanger et al. (1995) and Eastwood et al. (2010) provide careful discussions of both the theory and the empirics of the IR debate, a full review of which is beyond the scope of this paper.

It will suffice here to note that, following Barrett et al. (2010), an inverse relation between farm size and productivity may have three main explanations: (i) imperfect factor markets, (ii) omitted variables and, in particular, omitted controls for land quality, and (iii) statistical issues related to the measurement of plot size. Imperfect factor markets (labor, land, insurance) are linked to differences in the shadow price of production factors that in turn lead to differences in the application of inputs per unit of land, in ways that are correlated with farm size. Much of the earlier contributions to the IR debate focused on testing this type of explanation. Assunçao and Ghatak (2003) demonstrate how theoretically unobserved heterogeneity in farmer quality may explain the observed differences in productivity. Other studies (e.g. Bhalla and Roy, 1988; Benjamin, 1995) have challenged the existence of the IR based on the observation that when land quality controls are introduced in the analysis, the strength of the IR often diminishes substantially or vanishes altogether. Barrett et al. (2010) utilize a dataset that includes laboratory measures of soil testing to conclude that in fact only a very limited proportion of the IR can be explained by differences in land quality. Lastly, attention has been drawn to the possibility that the existence of the IR may be a statistical artifact deriving by measurement error in land data (Lamb, 2003). A similar explanation is also hinted at by Barrett et al. (2010), after failing to explain the observed IR otherwise.

For the IR to be partially or fully explained by errors in land measurements, smaller farmers would have to systematically underreport land area with respect to larger farmers, thus resulting in artificially inflated yields in the bottom part of the distribution. However, as reported by De Groote 3
and Traorè (2005), small farmers tend to overestimate their land holding – while large farmers tend to underreport – hence increasing the likelihood of analysts finding an even stronger inverse relationship in empirical studies based on more accurate measures.

Land area measurement is one of the fundamental components of agricultural statistics, and it is therefore not surprising that the interest of agricultural statisticians in the possibility of applying technological innovations such as satellite imagery and GPS devices to land area measurement is growing exponentially with the increasing affordability and precision of these technologies and their applications. Kelly et al. (1995) have long identified the use of GPS has having the potential to contribute to making land area measurement a much less costly and time consuming exercise than traditional methods. An early study mentioning a comparison of GPS and self-report plot measures is Goldstein and Udry (1999). They only refer to this in passing in a study of agrarian innovation in the Eastern Region of Ghana, reporting a very low correlation coefficient of just 0.15 between the two measures. They explain the result with the fact that traditional land measures in the region were based on length only (ropes), and as land became more scarce local farmers found it difficult to translate that to a two dimensional measure (hectares).

Keita and Carfagna (2009) provide a discussion of the performance of different GPS devices compared to traditional methods (rope and compass), which they consider the „gold standard‟. Their evidence confirms that GPS devices allow measuring farm size with enough accuracy compared to traditional and objective land measurement methods such as compass and meters. They conclude that the GPS is a reliable alternative to traditional measures (80 percent of the plots in their sample is measured with negligible error), but that on average GPS measures tend to underestimate plot area somewhat. The main reasons for errors in GPS measures detected by this study are the density of plot tree canopy cover and to some degree weather conditions at the time of measurement.

In a somewhat different application in the context of Peruvian market access self-reported data _vis a vis_ “true travel time” using GPS, Escobal and Laszlo (2008) show how if the error is correlated with the main outcomes of interest the conclusions of the analysis may be biased and driven by a spurious correlation. That is because the deviation between the „true‟ travel time and the respondents‟ estimate is determined by observable socio-economic variables related to the outcome of choice. Gibson and Mckenzie (2007) show evidence of the non-random distribution of measurement error in several of the distance and location studies they review, and demonstrate how the use of GPS aids can help overcome problems of measurement in data collection efforts.

GPS measurements are of course not immune from problems themselves. Possibly the most important issue is the fact that it is generally not practical and too costly to measure all the plots owned by a household. Some plots may be distant from the place of the interview (usually the household‟s dwelling), and respondents may not have the time or be willing to accompany the 4
enumerators to all the plots. Even if they were, the operational costs and travel time required to record GPS measures for all plots are likely to be prohibitive for most survey operations. This raises some analytical concerns, in the form of biased estimates, if the plots that are not measured are systematically different from the ones that are measured. We do find evidence of such bias in our data, and in the next section we discuss how we dealt with the issue.

# **3. Data source and descriptive statistics**

The data for this paper come from the Uganda National Household Survey (UNHS) round implemented by the Uganda Bureau of Statistics (UBOS) in 2005-2006. The UNHS is a multi-purpose household survey with a sample of 7,500 households, selected following a stratified sample design that identified 753 enumeration areas (UBOS, 2009). One special feature of this survey that makes our analysis possible is that it contains plot level information on agricultural land area measured through both GPS and farmers‟ own estimates.

Some 5, 714 of the survey households are located in rural areas and cultivate land. The total number of plots with self-estimated measure is 13,959 and about 65 percent of these (9,173 plots) have a corresponding GPS measure<sup>3</sup> . The agricultural production section, however, only contains information gathered at the household/farm level. Thus, the analysis in this paper is carried out partly at the plot level, and partly at the household/farm level. We use the former to analyze the difference between land area measurement using farmers‟ estimate and GPS, since it is at the plot level that the two measures are collected. The household/farm level analysis is more suitable to investigate the consequences of the bias in land measurement on the IR, since key farm input and output data are only available in the survey at this level, not allowing the calculation of plot-specific productivity measures.

To be able to run the analysis maintaining a consistent sample throughout, we therefore restricted our sample further to 5,767 plots for which we have complete information on both type of measures for all the plots cultivated by the household. In the farm level analysis, for which we also drop 42 households with negative farm profits (equivalent to 1.5 percent of the sample), we end up with a sample of 2,860 rural households for which we have both non-zero land area measures for the entire households‟ landholdings.

Table 1 reports key summary statistics for the plots for which we have information on both types of area measurements, along with the mean and standard deviation (in acres) of plot size measured through GPS, self-reporting, and the absolute and relative difference between the two measures. For simplicity of presentation, we will take the GPS measure as the benchmark and talk of farmers over- (or under-) reporting plot size whenever the area self-reported is larger (smaller) than the area measured by GPS. We do acknowledge however that the GPS measure may also be subject to a certain degree of inaccuracy (Keita and Carfagna, 2009).

> 3 A Garmin 12XL GPS device was used by the survey teams to collect plot area data.

5
On average the two methods produce strikingly similar estimates of land area. The average size of plots using GPS is 2.24 acres, a mere 0.11 acres (equivalent to 4.9%) larger than the area reported by farmers. The sample level means however mask pervasive differences in measurement that emerge at closer scrutiny. In the overall sample, farmers overestimate plot size in 54.12 percent of the cases (or 3,121 plots), and underestimate it in 44.13 percent of plots (equivalent to 2,545 plots). For the remaining 101 plots (1.75 percent) the survey reports identical measures with either method. For the plots where a „positive discrepancy‟ is observed, namely a GPS measure larger than self-reporting, the amount of area overestimated is larger in absolute value (1.07 acres on average, or 35.1 percent) than for the plots for which the bias is negative (-0.67 acres or 47.2 percent).

The fact that we dropped a substantial number of plots from our analysis because of gaps in the GPS measurement raises some concerns regarding whether this may introduce a source of bias in our analysis. This intuition is partially confirmed by an inspection of the summary statistics for the two sets of plots. Annex Table 1 reports the means and t-tests for the difference in means for some key plot and household characteristics. The plots that we had to exclude from the analysis because of gaps in the GPS measure are on average smaller than those we did include, they are more likely to be on a steep slope, and less likely to be protected by a fence. The heads of households to which these plots belong are somewhat older and less educated, and more likely to be female. Also, these plots belong to households that are on average smaller. These plots are therefore not randomly selected, which is what one would expect, since taking the actual GPS measurement of a plot requires a household member and enumerator to move for the site of the main interview to the location of the plot to take the GPS measurement. More distant, less accessible plots are therefore more likely to be excluded. These statistically significant differences in plot characteristics between the part of the sample we use and the part we had to discard suggest the presence of possible sample selection issues arising from these restrictions and impacting on the analysis of farm productivity. We will return to this point in the result section, to show how these issues to do not in fact appear to be affecting our results. The nonrandom selection of GPS-measured plots, however, does represent a challenge that future surveys employing these methodologies will have to find ways to confront.

Table 2 summarizes land measurement statistics at the household level. We report statistics for deciles of landholding to investigate how measurement bias plays out at different points of the distribution. This information will be important later, when we analyze the impact of land measurement bias on the IR. The last column of table 2 reports the discrepancy in percentage terms. According to this measure, the magnitude of the discrepancy appears to increase monotonically as one moves from the bottom (smallest landholders, -97 percent) to the top deciles (largest landholders, 19 percent). Up to 4.57 acres of farm size (the seventh decile), the bias is on average negative, whereas it becomes positive in the top three deciles. There is therefore a pattern in the direction of the bias, with 6
smaller farmers generally over reporting their land relatively more than larger farmers, and with the largest farmers actually under reporting land size.

These findings go in the same direction as the results of De Groote and Traorè (2005) for Southern Mali. As stated above, De Groote and Traorè find that there is an approximate linear negative relationship between measurement error and plot size. Farmers have a tendency to overestimate small plots (which they define as below 1 hectare<sup>4</sup> ) compared to larger ones, which they somewhat underestimate. Also, the GPS and self-reported plot area measures in our sample display a correlation of 0.97 (which drops to a more reasonable, but still respectable, 0.77 when we trim the right end of the distribution of a few very large plots), well above the 0.15 found by Goldstein and Udry (1999) in their Ghana dataset.

One additional issue in our data, that is immediately apparent from the visual inspection of the distributions of the two land measures in Figure 1, is the considerable tendency of respondents (or enumerators) to round their reported plot size to nearest acre or half acre. This „heaping‟ in the response pattern is not uncommon (Roberts and Brewer, 2001) but we suspect it may be particularly important in the case of land measurement since it is bound to matter proportionally more to the left of the distribution, as the same amount of rounding represents a larger percentage of the actual plot size.

Figure 1 also confirms that the two distributions are, overall, quite similar. However, while the means are not much different, at specific points the distributions deviate considerably, in a way that appears to be driven by heaping in the self-reporting distribution as opposed to a smooth curve for the GPS measure. Finally, the comparison of the two distributions appears to support the case for treating the GPS measure as the more accurate of the two.

The systematic patterns in the difference between land measurements we have observed above have the potential to introduce a bias in the estimation of agricultural/land productivity. Reasoning through the data it is apparent, as we already mentioned, that the kind of pattern we observe in our data should, if anything, generate a bias opposite in sign to that needed to corroborate the IR hypothesis. If small farmers report to be cultivating more land than they actually are, their „true‟ yields are actually even larger than what one would compute using self-reported land quantities. To explore that point descriptively, Figure 2 draws the relationship between deciles of cultivated land and farm yields (computed as the ratio of the value of agricultural production over farm size). The slope of both lines is negative, pointing to an inverse yield-farm size relationship in both cases, but the line is even steeper when the GPS land measure is used.

Table 3 summarizes farm yields computed using GPS and self-reported land areas. Farms are categorized as small, medium or large. Small farms, those cultivating landholdings smaller than1.45

> 4 1 hectare is equal to 2.47 acres.

7
acres exhibit systematically higher yields when area cultivated is measured through GPS as compared to self-reporting. The distance is reduced for medium farms, whereas large farms have lower yields measured with GPS than those obtained through farmers estimate.

The inclusion of a more accurate measure of land area in this dataset seems to be strengthening the empirical case for the existence of an inverse farm size productivity relationship, rather than weakening it. This is consistent with what we expected after looking at the distribution of the discrepancies in the two measures, but appears to contradict the discussion in Barrett et al. (2010) and the analysis in Lamb (2003), who finds that the IR disappears after introducing random effects which he hypothesizes capture the influence of measurement error.

# **4. The econometric approach**

In order to deepen the analysis of (a) the characteristics and determinants of the discrepancy between our two land measures, and (b) the implications of measurement bias on the robustness of the IR hypothesis, we estimate the two models specified below.

As in Deininger et al. (2011), to identify what are the factors affecting the difference between the two measures we estimate the following function, at the plot level: _e j_  _x j_  _u j_ Where _e j_ is the plot size specific difference between the GPS and the self-reported measure, _x j_ is a (K+1)-row vector of control variables with „1‟ as its first element,  (  0 ,  1 ,...,  _K_ )' is vector of parameters to be estimated. _u j_ is a two-sided error term representing white noise The controls used in this regression include a set of characteristics of the household head (age, education, and gender) to proxy respondents‟ characteristics that are deemed to influence the ability to accurately report land size. We also include plot size, and its squared term, to test whether the relationship observed in the descriptive analysis holds in a multivariate framework, and a dummy reflecting whether the self-reported land variable is a round number, to capture the impact of rounding. We include information on whether the household is involved in disputes over land ownership, as we expect such households to have less information or interest in these plots. Topography will also affect land estimate by farmers, as steep plots may be more likely to be subject to measurement error. Finally, we also add PSU dummies to control for idiosyncratic differences across survey teams and supervisors and for possible environmental and geographic factors.

Next we estimate a standard model for testing the existence of the IR, and to understand how land measurement error weakens, eliminates or reinforces this empirical evidence. Our model is based 8
on the one originally proposed by Binswanger, Deininger and Feder (1995), and not dissimilar from the approach used by several others including, most recently, Barrett et al. (2010). We estimate the following function at the household level: _A_ where<sup>_Y_</sup> _i_ represents net agricultural revenues for each household _i_ , _i_ the total area operated, _X i_ denotes a vector of households‟ characteristics that influence production such as the availability of family labor, the gender, age and education of the household head, value of inputs used, and a set of land quality variables, R is the rounding effect when net revenues per acre of area cultivated are measured with land size as reported by farmers, and<sup>_u_</sup> _i_ is the error term. We estimate two versions of this relationship, one using GPS and the other one with the self-reported land measure, and compare the two to gauge the impact of differences in measurement on the IR, which is captured by the coefficient on the land size variable. A negative coefficient on the land area variable indicates the presence of the IR. The further below 0 the coefficient, the stronger the IR. As in the previous model, we also include PSU fixed effects to control for survey team and local environmental effects.

The left hand side term - net agriculture revenues per acre - is computed as the value of total crop production net of value of variable inputs (hired labor, seeds, organic and inorganic fertilizers, chemicals, and animals rented for plowing), divided by the amount of land cultivated. While we maintain this is the preferred way to calculate net revenues, some may argue that subtracting hired but not family labor may give an unfair advantage to small farmers who rely mainly on the latter. We therefore also tried running our estimates without subtracting hired labor costs from gross revenues and the results (not reported) did not change to any significant extent.

Regarding the terms on the right hand side, we expect productivity to be positively related to the use of variable farm inputs, including hired labor. Given the supportive evidence provided by several of the contributions to the inverse farm size productivity debate (Lau and Yotopoulos 1971; Berry and Cline 1979; Kutcher and Scandizzo 1981; Carter 1984; Eswaran and Kotwal 1985; 1986; Barrett 1996; Udry 1996; Benjamin and Brandt 2002), we expect labor market imperfections to give an advantage to farms able to rely on family labor, and hence a positive sign on the coefficient on this variable.

To control for various aspects of land quality, variables on farmer-assessed soil quality, steepness and irrigation of the plots are included as regressors. The soil quality variable is computed as the share of total cultivated land the farmer reports being in plots with good soil quality. The share of steep land is similarly computed using plot level data, and taking the sum of plot size with steep slope as a share of the total landholding. In the same fashion the share of land irrigated is constructed 9
dividing the area of the cultivated plots reported to be irrigated by the total cultivated acreage. The obvious expectations concerning the regression coefficients on these variables are that good quality, irrigated land will be associated with larger profits per acre, whereas greater shares of steep land will, other things equal, be associated with lower levels of productivity per unit of cultivated land.

The final set of variables in the regression relates to household characteristics. The age of the household head is normally expected to reflect farming experience and therefore be positively related to farm productivity. It is also possible that older age may be related to reduced physical strength, health problems and hence reduced ability to farm the land, but the experience aspect usually dominates. Education should clearly affect positively farmers‟ productivity and welfare, while the expectation is for female headed households to be less productive because of a wide variety of factors ranging from discrimination in input and output markets to unfavorable family composition. Where the female headship is due to the presence of a migrating husband sending remittances back home that can be invested in farming, however, the impact on farming and productivity may in fact be positive.

# **5. Empirical results**

The results of the estimation of model (1) are reported in Table 4. Confirming the results of the descriptive analysis in section 3, the data show a positive association between plot size and the difference between GPS and self-reported land measurements in levels. This discrepancy increases with farm size: larger farms have a tendency to under-report, while small farms tend to over-state the size of their landholdings.

The other signs are also as expected. The presence of rounding contributes to increasing measurement error, as we hypothesized based on the heaping displayed by the distribution of selfreported plot size in Figure 2. While the education and gender of the household head variables are not significant, head‟s age matters. Older heads are likely to be less accurate in their reporting of plot size. Households who are involved in disputes over land are also likely to make larger errors in selfreporting, which we hypothesize is due to the fact that such disputes diminish their interest, access, and in general knowledge of plot characteristics. Contrary to expectations the demarcation of the plot with a fence does not seem to reduce the error in land self-reporting; the coefficient of the dummy if the plot has a fence is positive and significant thereby suggesting a larger error for those plots. Finally, the steepness of the plot does not appear to significantly influence measurement bias.

Table 5 presents the results of the net revenue regression in model (2). In column (1) land is measured with the traditional respondent self-report, whereas column (2) is based on the GPS measure of land size. The main variable of interest in this model is the (log) of land size, as it is this coefficient that captures the size-productivity relationship, with a negative coefficient pointing to the existence of an inverse relationship. The estimated coefficients are -0.62 in the specification using self-reported 10
land size and -0.83 in the specification using the GPS measure of agricultural plots. Both estimates therefore support the IR hypothesis. When the GPS measure of farm size is used, however, the absolute value of the coefficient increases, indicating an even stronger IR.

The inclusion of hired labor and inputs on the right hand side poses problems as they may capture part of the effect of market imperfections, not allowing for their full effect to be reflected in the farm size coefficient<sup>5</sup> . To check for the extent to which this problem might affect our results we run the same regression without these variables and the key results (not reported) did not change. In both specifications, the coefficient of land size decreases of 0.1 but remains negative and statistically significant.

The hypothesis according to which the IR would be a statistical artifact due to small farmers under-reporting their farm size is therefore strongly rejected by the data. In our sample, small farmers in fact over-report land size, and it is the very large famers who are actually more likely to underestimate their holdings, thus resulting in artificially higher yields. When more accurate land measures are used thanks to the introduction of GPS devices, the estimated slope of the function becomes steeper indicating an even stronger IR than what one would conclude based on similar estimates performed using farmers‟ self-reporting.

As expected, good soil quality shows a positive association with farms profits, which remains stable across specifications. The irrigation and steepness variables, on the other hand, have the expected signs (positive for irrigation, negative for steep land) but the estimated coefficients are not statistically significant.

As discussed in Section 3 above, one issue with our data is the sample selection bias introduced by dropping from the productivity analysis the households for which we do not have both measures for all plots. To investigate whether this may be a factor invalidating our main findings we re-estimated model (2) using the entire sample, and tested (a) whether the group means of predictors estimated using the two samples are equal, and (b) whether the main coefficients of interest for the IR (i.e. the coefficients on the land variable) are equal. Results are reported in Annex Table 2.

The Wald test rejects the null hypothesis that all coefficients are equal for both samples, which one would expect given the systematic differences between the two samples we reported in Annex Table 1, and discussed earlier in the paper. What matters for our key results, however, is that the test fails to reject the null for the land coefficient. In other words, the IR estimated using the self-reported measure is as strong on the full sample as it is on the restricted sample for which we have complete GPS information. For productivity analysis at large, however, the rejection of the test of equality between the two runs of the model does point towards the need for future surveys to solve the

> 5 The input variables also pose possible endogeneity problems being choice variables for the farmers.

11
selection issues related to GPS measurement of plots, as that is bound to matter for specific aspects of the analysis.

One final concern relates to the possibility that larger farms be concentrated in remote and unfavorable agricultural areas, or that market imperfections leading to the IR may be confined to particular regions. We investigated whether that appears to be the case in our data, by running our analysis separately for the four macro-regions for which the UNHS is statistically representative (Central, Eastern, Northern and Western Uganda). Annex Table 3 presents a summary of the analysis. For brevity we only report the coefficient of land size, which is our variable of interest. The specification is the same as that described in model (2) and reported in Table 5 for the full sample, with the same explanatory variables included but not reported. The top panel of Annex Table 3 reports the results of the IR between net revenue of crop production per acre computed using the self-reported land area variable, for each of the 4 regions. The bottom panel shows the corresponding statistics for the specification that uses the GPS area measurement. As in Table 5, we note that in all regions the IR holds regardless of the specification, but that it is stronger when the GPS area measured is used. Our results do not therefore appear to be sensitive to the effect of possible socio-economic or agroecological differences across regions.

# **6. Conclusions**

The hypothesis that the inverse relationship between farm size and productivity may just be a statistical artifact, linked to problems with land measurement error, is rejected by the analysis presented in this paper. Contrary to earlier conjectures, we find that the empirical validity of the IR hypothesis is strengthened, not weakened, by the availability of better measures of land size collected using GPS devices. Lamb (2003) concludes that by controlling for measurement error in land size, the statistical case for the IR disappears. This paper has shown that introducing rigorous controls for land _quantity_ does not affect the evidence concerning the IR, which is in fact strengthened when the better land data are used.

We also explored how farmers‟ self-reporting of plot size varies systematically with the size of their holdings and other household and land characteristics. We conclude that in Uganda small farmers tend to over-report plot size relative to medium-sized land-holders, while the largest farm groups under-report plot size on average. This is consistent with earlier evidence from Mali reported by De Groote and Traorè (2005).

Self-reported measures of land size are notoriously imprecise. In large household surveys in developing countries, however, they have for a long time been the only option available to practically collect data on the physical dimension of the plots owned or cultivated by the household. More 12
recently the availability of affordable and more reliable GPS devices has made GPS measurement a practical alternative that is increasingly being applied in surveys worldwide.

Being able to measure land with any degree of accuracy is clearly of outmost importance in economies that are largely agricultural based and for communities that derive a large share of their livelihood from agriculture and for whom land constitutes the main, when not the only, capital asset. In particular, an accurate measure of land size is necessary if one is to measure agricultural productivity with any degree of confidence.

This paper has shown that GPS technologies clearly hold promise for improving the accuracy in the collection of land size measures in the context of large household surveys. On the other hand, while we are not able to account in full for the determinants of the deviation between GPS and selfreported measures, we do find that self-reported land measures are a reasonable alternative in a well conducted survey, particularly for medium-sized farmers. The overall distribution as well as their mean and standard deviation, are fairly close to each other, and the measurement error did not change the substance of our productivity analysis. The respondents‟ rounding of responses can however create fairly serious differences in measurements, particularly when plots are small, as is the case here (but also in most of the developing regions).

The continuing fall in the price and increasing precisions and reliability of GPS devices make them an increasingly attractive element of every survey team toolbox. For mainly logistic reasons, however, GPS readings are hardly ever taken on all plots, and this raises concerns on the potential selectivity bias resulting from measuring only a sub-set of plots. While allocating adequate resources could go a long way in ensuring that this bias is reduced, farmer‟s self-reported measures must also be collected possibly together with information on the possible sources of the bias, to complement the GPS estimates and correct for potential biases. How to do that in practice is a subject that warrants further investigation.

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