# _Group 3: Imputation-based Data Sets_

When inequality statistics are imputed into country-year cells, our focus should be on understanding both the imputation methodology and the inputs that are used to generate the imputed values. Both will determine what type of inequality (income or consumption; household or individual; per capita or equivalized) is really being presented, and how reliable the estimates are likely to be. Panel C of Table 2 reports on some such questions for SWIID, the only imputation-based data set under review in this special issue.

In its use of imputation to construct full annual series of inequality statistics, SWIID differs greatly from any of the other databases reviewed in this issue. We describe the series as full because an inequality measure is presented for every single year in a given interval, regardless of whether a survey, census or any other data collection exercise actually took place in that country in that particular year. One can immediately appreciate both how such series would appeal to macroeconomists running panel cross-country regressions, and how they might worry micro-economists specializing on the accurate measurement of poverty and inequality. For each country-year cell, SWIID reports annual gross and net income inequality, measured by the Gini coefficient.

The imputation procedure involves estimating ratios of Gini coefficients – sometimes across countries, and sometimes between one welfare concept (e.g. net income) and another (e.g. gross income) – incorporating all the information available to determine both an inequality estimate and a standard error in each case. Multiple imputation methods (following Rubin, 1987 and 1996) are used, which essentially rely on assuming that ratios between different inequality measures are constant, or stable, and can therefore be used to predict those variables when they are not observed. Solt (2009, 2014) describes this method in some detail, and Jenkins (2015) reviews it. A key issue, to which we shall return, is the tension between two “competing demands” (Jenkins) faced by any such exercise. These are (i) that information be pooled from a sufficiently large group of actual observations (data inputs into the imputation), so that the Gini ratios are robustly estimated; and (ii) that information determining each particular Gini ratio be drawn only from the most comparable set of observations possible, so as to avoid polluting the prediction with ratios from extraneous countries or periods, which actually bear little resemblance to the true object being estimated. Even if all observations in a data set are used, the same tension can be rephrased in terms of the weights assigned to each observation.

At some level, these competing demands are inherent to _any_ imputation exercise: essentially inferring ‘data’ where none is actually available, on the basis of observed relationships between other data that are actually observed. On the one hand, since the relationships (e.g. between gross and net income inequality) vary over space and time (e.g. between Europe and Africa; or between the 1970s and the 1990s in North America), constancy relationships should ideally be drawn from as close to the empty cell to be filled as possible. On the other hand, estimating relationships from very small neighborhoods may be either too imprecise or downright impossible, where data is particularly scarce. As with other imputation methods, therefore, the one used by SWIID is likely to be at its most reliable precisely where it is least needed – i.e. in filling in occasional gaps in otherwise data-rich environments, such as 12