Correlated non-classical measurement errors, ‘Second best’ policy inference, and the inverse size-productivity relationship in agriculture

We show that non-classical measurement errors (NCME) on both sides of a regression can bias the parameter estimate of interest in either direction. Furthermore, if these NCME are correlated, correcting for either one alone can aggravate bias relative to ignoring mismeasurement in both variables, a ‘second best’ result with implications for a broad class of economic phenomena of policy interest. We then use a unique Ethiopian dataset of matched farmer self-reported and precise ground-based measures for both plot size and agricultural output to re-investigate the long-debated relationship between plot size and crop productivity. Both self-reported variables contain substantial NCME that are negatively correlated with the true variable values, and positively correlated with one another, consistent with prior studies. Eliminating both sources of NCME eliminates the estimated inverse size-productivity relationship. But correcting neither variable generates a parameter estimate not statistically significantly different from that generated using two improved measures, while correcting for just one source of NCME significantly aggravates the bias in the parameter estimate. Numerical simulations demonstrate that over a relatively large parameter space, expensive collection of objective measures of only one variable or correcting only one variable's NCME may be inadvisable when NCME are large and correlated. This has practical implications for survey design as well as for estimation using existing survey data.