Family time.

IMAGINE a society with only three people. Each of them has an annual income of $50,000. At some point, two of them marry. Has the income distribution changed?

The answer, of course, is no. Before and after the marriage, each person has $50,000 in income. The distribution remains exactly the same.

But government statistics would suggest otherwise--that the share of total income has shifted dramatically in favor of the rich. That's because most government surveys track data for "family units," not individuals. And the number of individuals per family unit can vary greatly, depending on marital status, children, and other factors.

My colleague Aparna Mathur and I have presented evidence in these pages that many of the statistics commonly used to paint a picture of middle-class misery are misleading. The best measure of how the middle class is doing, we argued, is consumption, and consumption has been doing just fine.

Our earlier work accepted the standard assumption that the family unit is the correct level of analysis. In a new paper we have just completed, however, we find that this assumption is highly misleading.

The problem is that, much to our surprise, there is enormous variation in family size across income distribution. Family units with higher incomes are more likely to contain a married couple, and more likely to include children. In 2005, for example, the average family unit in the lowest quintile had 1.8 individuals. The average family unit in the top quintile had 3.1 individuals. So while those at the top have more resources, those resources come from more earners and are used to feed more people.

In the nearby chart, drawn from our paper, we estimate the growth in consumption since 2000 for individuals in each quintile, adjusting the data to account for the fact that family units have different sizes. The data now tell an even more striking story than our original work, which did not adjust for family size. It is not those at the top who have seen their economic well-being increase fastest since 2000, but rather those at the bottom. Those in the middle have seen their incomes grow faster as well.

As we show in our paper, failing to adjust for family size makes the consumption growth rate of the rich appear slightly higher than that of everyone else. But the growth rate for all income quintiles is quite healthy. Thus, the notion that all the benefits of our economic growth are going to the rich is incorrect. It is true, as the New York Times recently wrote, that consumption growth is "unbalanced," but it is not clear in which direction. The answer depends on whether you adjust for family size.

The day may come when the fruits of our economy are spread so thin that additional government redistribution is demanded by all men of good conscience. But today is not that day.

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