The measurement of income inequality plays a pivotal role in the assessment of economic welfare and the design and implementation of social policies. A primary input of such measurement is data provided by household surveys. It is a well-documented fact that in these surveys some variables are measured with errors. Regarding income, a commonly found problem is that some people refuse to answer income questions. In countries where the proportion of income non-response is high, inequality, poverty or other measures constructed using income may give a distorted picture if non-response is not handled appropriately. What should be done with cases where income is missing? How do different methods used to deal with this problem affect inequality measures? These questions could be of paramount importance in particular countries, such as some Latin American countries, allegedly those with the world highest inequality levels. In countries like Argentina, Chile, Colombia, Costa Rica, Ecuador and Venezuela, income non-response rates are well above 5% and, in some cases, higher than 10%. In other countries, like Honduras and Panama, income non-response rates are relatively low in general, but are high (more than 10%) for particular labour categories such as self-employed and firm owners. How much of reported income inequality is due to an incorrect treatment of measurement errors? The issue of dealing with missing data has been the main topic of several studies, not only in economics but also in sociology and political sciences, where individuals do not provide answers to questions related to income, political participation and racial issues, for example. The issue of how different correction methods affect inequality measures has received, comparatively, less attention though its relevance is paramount. Even comprehensive works on household surveys, such as Deaton (1997), pay little attention to issues related to the effect that quality of the data has on economic inferences in general and inequality inferences in particular. Some other works mention this problem though they do not propose any mean to solve it. Gottschalk and Smeeding (2000), for instance, recognise that different patterns of income non-response (depending on the relationship between the probability of non-response and actual income level) may affect inequality measures differently and acknowledge the difficulties of knowing the exact patterns in each case. Empirically, the problem of correcting for income non-response is not about finding a method to correct for such a non-response, but about knowing the pattern of this non-response or, in other words, the relationship between the probability of non-response and the actual income level. Many methods have been proposed to correct for income non-response. All of them make particular assumptions regarding the pattern of missingness. However, in practice it is generally very difficult to verify such assumptions, as in most cases missing data is not gathered by any other mean (e.g, other surveys or through administrative sources). What happens when the patterns of missingness assumed by such methods do not coincide with the actual one? How are inequality measures affected in these cases? The answers to these questions, related to the robustness of correction methods, are relevant if we want to have an idea about how measured inequality levels differ from the "true" levels of inequality. This paper aims to analyse how, under different patterns of missingness, several methods generally used by economic researchers and National Statistical Offices may produce different inequality levels. From an empirical point of view, the paper establishes the biases that such methods introduce under specific patterns of missingness. In this respect, it is an exercise to test how inequality estimations change when the assumed pattern of missingness does not coincide with the actual one. To achieve these objectives the paper develops a simulation approach. We use (non-random) subsamples of workers that do report their incomes from the Argentinean Permanent Household Surveys. On these subsamples we simulate several patterns of income non-response and apply different methods to correct for it (e.g., deletion of missing data, simple OLS regression imputation, hot-deck, etc.). Because we know the exact value of workers' incomes, we can compute "true" and "imputed" income inequality to assess the "accuracy" of the different methods to produce inequality measures. The results obtained show that inequality measures can be severely affected if the missing data generating processes (mdgp) assumed by imputation methods do not coincide with the actual mdgp (simulated on the data). The biases introduced depend on the method used under different simulated mdgp (i.e. for some mdgp a method may be relatively good in terms of inequality measures, while for other mdgp may produce significantly biased measures), on the shape of the actual inequality distribution (i.e. some methods perform better for years with higher actual inequality), and on the inequality measure used (i.e. some inequality measures are more “stables†than others to certain types of data contamination)
