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The issue with consumption as a metric of inequality is that it struggles to incorporate saving.

'Snapshot' measures of consumption across a short period, like a year, fail to measure savings altogether. If we both make £50k in a year, but you spend it all and I put £5k away, the value of your consumption is £5k more than me; but obviously that's not an inequality that needs to be remedied by policy, we've just made different choices of what to do with the same endowment.

It's normally assumed that this can be fixed by thinking about lifetime consumption. When I hit retirement and start to draw down my pension, I'll take out that £5k and consume it, whereas you won't have the chance to because you didn't save; so our lifetime consumption will even out.* But there's still two deep problems with this.

(1) It's incredibly difficult to measure and to design policy around. For instance, a consumption tax can only efficiently target lifetime consumption if it remains constant over time. If I think a tax-cutting government will come in next year, I'll just put off big-spending purchases by a year - effectively tax-dodging across time, rather than across borders as is the norm. And across a whole lifetime, if I make the reasonable guess that taxes (once introduced) only tend to increase in the long run, I'll save less for retirement and consume more now, to get more lifetime consumption overall. A variable consumption tax will reduce inequalities between people to some degree, but to a bigger degree it will just redistribute consumption within one person's lifetime, and not even in a way that any one government can control.

(You might argue that all taxes are inefficient, but this is a particular problem for consumption taxes, because consumption is entirely under the taxpayer's control. By contrast, since income largely isn't a matter of personal choice but rather career progression, most of us don't really have the option to get all our income now to pay less tax on it: you get the highest incomes at the end of your career no matter what.)

(2) Even if you try to assume away the above, no matter how theoretically optimal your measurement and policy design are in practice, consumption will always ignore saving for after your lifetime. The classic example is buying a house to pass on to your kids: even if you live in the house, and so 'consume' part of the good, your consumption does not accurately measure the value of the good for you; you'd also have to find a way to incorporate the expected future consumption of your heirs. More blatantly, if I have ten million in investments held in a trust fund for my kids, I'm not consuming any of that, but it is not therefore irrelevant to the question of inequality. Sumner is making the standard economist's assumption that economic behaviour can be modelled by utility-seeking over a lifetime; but no matter how sophisticated your utility function, this will never measure one of the crucial motivations of economic behaviour, which is the desire to leave something better to your children.

Measuring inequality in terms of income or wealth is economically suboptimal, but has two crucial advantages. First, practically, they incorporate savings of all kinds, while allowing for policy flexibility if you want to exclude some savings and encourage certain practices (tax breaks for pensions are an example). Second, philosophically, they measure Rawlsian 'primary goods' and so avoid making any assumptions about utility while not thereby getting sucked into making value judgments about which forms of consumption are better. (And of course, income tax demonstrably works in its primary function of raising revenue for the state, whereas consumption taxes would struggle here.)

*There's technicalities here due to inflation and capital gains, but you get the jist.

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