incomes) is called the _sharegain_ .<sup>9</sup> When redistribution is significant, we expect the market-income poor decile to have positive (and large) _sharegain_ ; _sharegain_ should monotonically decrease in higher market income deciles, eventually turning negative.<sup>10</sup> Intuitively, a positive _sharegain_ simply means that a given decile gains though the process of redistribution; a negative, that it loses.

# Treatment of state pensions

A further issue concerns how to take into account the (often large) fraction of government transfers that are pension payments. To the extent that state pensions reflect actuarially fair contributions made by beneficiaries and their employers and have no redistributive component, state pensions are properly considered to be part of market incomes. Pension payments have a redistributive component to the extent that payments to the poor exceed their contributions and payments to the rich fall below them. The larger the redistributive component, the greater the justification for including pension payments as part of redistributive transfers and not part of market incomes.

Prior research takes an eclectic approach to the treatment of pensions. Iversen and Soskice (2006) and Lupu and Pontusson (2011) exclude from the data any households not headed by individuals 25 – 59 years old. These are households that do not receive pensions, but may be making pension contributions. This approach has the advantage of excluding households for which it is difficult to establish the redistributive nature of the government transfers that they receive. The disadvantage of this approach, however, is that the excluded households are both politically salient (the elderly vote disproportionately in many countries) and an important part of the income distribution of the country. To the extent that incomes of older households are distributed differently than incomes of other households, their exclusion distorts the income distribution that is the subject of the analysis.

For example, income surveys in the United States regularly show that older households have higher incomes than younger households. Assume that those higher incomes are the product of actuarially fair (non-redistributive) pensions. The incomes of these pensioners could be (indeed, to some extent are) excluded from taxation, while the non-pensioner households with the same market incomes are subjected to taxation. In this case, the exclusion of (high income) pensioners from the analysis exaggerates the measured extent of redistribution, since high income pensioners pay lower taxes than the high income households included in the analysis.

Because of this, other researchers (e.g., Milanovic 2000, Shayo 2009 and Scervini 2009) include all households in the sample. That is, instead of assuming that the distribution of market, gross and disposable incomes among pensioner households is the same as among other households, they assume that pensions are part of market income.

> 9 Consequently, the _sharegain_ when we go from marketP income to disposable  income will be for LIS countries: Disposable   - _brutto_ MarketP income  = all social transfers except social retirement benefits + all private transfers - payroll taxes - direct taxes. For the non-LIS countries, the sharegain will be equal to Disposable  - net MarketP income = all social transfers except social retirement benefits + all private transfers. For both  LIS and non-LIS countries the difference between gross and marketP income will be the same: all social transfers except social retirement benefits + private transfers.

> 10 Negative _sharegain_ means that a given decile’s share in disposable income is less than in market income. This would typicallly be the case for top market income deciles.

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