Correlated Non-Classical Measurement Errors, Second Best Policy Inference and the Inverse Size-Productivity Relationship in Agriculture

We show analytically and empirically that non-classical measurement errors in the two key variables in a hypothesized relationship can bias the estimated relationship between them in any direction. Furthermore, if the errors are correlated, correcting for either one alone can aggravate bias in the parameter estimate of interest relative to ignoring mismeasurement in both variables, a second best result with implications for a broad class of economic phenomena of policy interest. We illustrate these results empirically by demonstrating the implications of mismeasured agricultural output and plot size for the long-debated (inverse) relationship between size and productivity. Our data from Ethiopia show large discrepancies between farmer self-reported and directly measured values of crop output and plot size; these errors are strongly, positively correlated with one another. In these data, correlated non-classical measurement errors generate a strong but largely spurious estimated inverse size-productivity relationship. We demonstrate empirically our analytical result that correcting for just one measurement problem may aggravate the bias in the parameter estimate of interest. Acknowledgement : This paper benefited from comments by Marc Bellemare, Leah Bevis, Chris Boone, Brian Dillon, John Gibson, Kalle Hirvonen and seminar participants at the African Development Bank. Any remaining errors are the authors sole responsibility