The parametric welfare state

It occurred to me when working on the post below that Pareto distributions could also be a useful way of thinking about welfare state policies. This is fairly wonky, so if you’re not interested in the math digression then go ahead and skip to the second section below.

Income parameters

Pareto distributions are defined by two parameters (just as normal distributions are defined by mean and variance). The first of these is the the lower bound, which in an income distribution equates to the lowest level of income. The lower bound or floor is rarely zero and varies across countries, and even across time within a country.

The second is the shape of the curve, which in an income distribution reflects the relative concentrations of wealth in smaller and smaller groups. The more concentrated the society, the steeper the curve (typically called α, though I call it steepness here).

The charts below (source) show how each parameter can vary while holding the other constant.

They’re more abstract than my explanation above, but they can be read as ranging from low to high income as you move from left to right on the horizontal axis, and less to more people with that income as you move up the vertical axis (technically, it would be the probability of a randomly selected individual having a given income). So in the chart on the right, for example, the green line would represent a society with much greater inequality than the blue line, since the green society would have many more people earning the  lowest income.

Social policy

It strikes me that these two parameters – income floor and steepness of inequality – are also a useful way of categorizing both welfare state policies and the rancorous politics around them.

In the first category, policies such as actual welfare, Social Security, Medicaid and food stamps are all designed to put a floor under income. Disagreements about these sorts of policies go back through the time of Bismarck and all the way to the Poor Laws in England. The arguments have tended to be couched more in terms of morality than objective assessment, with many of the most vocal opponents willing to ignore facts that contradict their own preconceptions (I’m thinking of Alan Simpson here). The emotional charge of the opponents to these policies is for the moment much stronger than the response from supporters, though that may change once the Super Commission (itself a product of emotional arguments about the manufactured threat of the deficit) comes out with its recommendations.

The second category overlaps with the first to the extent that any policy that puts a floor under income will by definition reduce inequality. But it also includes programs intended to equalize access to opportunity like public education and Pell Grants, as well as government support for labor unions. It’s notable that there is almost no push back against the steady erosion of these policies in the US, while in the UK the steep increase in university tuition led to an earlier round of riots this year, and the public sector union strike was a significant event.

It may be that the greatest vulnerability of the two types of policy stems from the fact that their opponents are guided by a single set of beliefs (and a media system that supports and repeats those beliefs) that combines economic, political and emotional arguments, while their supporters are as fragmented as the policies themselves. But that would be another post entirely.

Coda: Pareto’s revenge

I didn’t realize until researching Pareto that he is an important figure in both economics and sociology, though he is much better known for the former. His passionate advocacy for laissez-faire economics and free trade made him both a bitter opponent of welfare policies and (for these and other reasons) a hero to Mussolini. I had that in mind when I built my discussion of the welfare state around his distributions – it seemed a nice bit of irony, though ultimately his ideas are the ones winning the day.

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