Three steps are taken to meet the objectives of the paper. First, we examine the differences between the two measures. Second, we determine to what degree the source of differences between self-reported area and GPS measures are due to observable factors. Finally, we compare the use of self-reported and GPS land measures in estimating the inverse farm-size productivity relationship to determine the implications for measurement error on agricultural analysis. To that end, we build on Carletto, Savastano and Zezza (2013) to systematically test the existence of an inverse farm sizeproductivity relationship in a number of different geographic contexts. The choice of the inverse productivity relationship is motivated by the fact it is a controversial relationship widely discussed in the agricultural development literature and land measurement has been noted as a potential issue in estimating the relationship (Lamb, 2003; Barrett Bellemare and Hou, 2010).

Meeting these objectives is possible because of recently collected, multicountry data coming out of the Living Standards Measurement Study—Integrated Surveys on Agriculture (LSMS-ISA). The project has collected relevant information from a number of countries in Sub-Saharan Africa to compare the approaches to land data collection and corresponding agricultural variables in order to assess the implications of such approaches to the analysis of agricultural relationships. We use data from four of the most recently completed surveys—Malawi, Uganda, Tanzania and Niger.

We find that there is a systematic discrepancy between GPS and self-reported plot areas with results indicating that, on average, farmers tend to over-report land area. This is particularly true for farmers at the lower end of the farm size distribution. While rounding of self-reported areas plays an important role in the misreporting as do household and plot level factors, this systematic discrepancy remains, and even strengthens, when controlling for these factors. Exploring the implications of these results on the analysis of the inverse productivity relationship, we find that, while in most countries the relationship slightly weakens, it does not disappear or change sign, thus confirming in each country, as well as in the pooled data, the persistence of an inverse farm size productivity relationship. Further, gradual introduction in the specification of additional control variables creates a greater divergence between the GPS and self-reported estimates indicating a level of endogeneity of the self-reported areas.

The remainder of this paper is organized as follows. Section 2 discusses the issue of land measurement and how it has been addressed in the LSMS-ISA surveys. The section also includes descriptive statistics comparing the measures and how they differ as well as an analysis of the difference between the two measures. Section 3 considers the implications for land measurement on agricultural analyses, particularly the widely analyzed inverse productivity relationship. Section 4 then provides conclusions regarding the implications of the analysis for studies that use selfreported land areas as well as the implications for collecting land data given time and monetary constraints.

# **2. Data and land measurement**

Suppose that the GPS measure, GPSi, represents the true area of a plot of land. Self-reported land area, SRi, can then be noted as follows: where εi is the error associated with that estimate. Even if classical measurement error can be assumed, where this error (εi) in self reporting is considered to be independent of the GPS-level of land area as well as all other variables in an economic model, estimates of economic relationships can be biased (Bound, Brown and Mathiowetz, 2001). In this section, we begin by carefully considering how land area is determined and the implications for the error in this measurement.

3