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Chris Dillow lays out the basic problem with living wages mandates. While having more money makes people happier, being unemployed is pretty awful. So whether mandating living wages can make sense will depend on how many people are forced out of work and how unhappy they are relative to the comparably small gains among the greater number of winners.
We can roughly quantify this. A paper by Nattavudh Powdthavee suggests that, in terms of wellbeing, we need a 30% rise in income to offset being unemployed. This means that if the average winner from a living wage gains 3%, we need at least 10 winners for every unemployed*.
You might think this condition is fulfilled. It is, if we consider only the wellbeing of those earning less than the living wage. But their higher wages come at the expense of profits. How much you're troubled by this depends on how you regard those employers. Are they exploitative tax-fiddling mega corporations, or are they small businesses struggling to get by?
And then there's the standard question about utilitarianism: is it legitimate to impose (largeish) costs upon a minority so that the majority enjoy other benefits?
He suggests that a guaranteed annual income - a variant on negative income taxes - may be the better option. When workers' non-work option improves, their bargaining position changes and wages have to go up.

This is true to a point, but it does require that voluntary unemployment (I don't want to work at going wages) makes you a lot less unhappy than involuntary unemployment (I want to work at the mandated minimum living wage, but nobody wants to hire me). And while that's almost certainly the case, if you put any weight on behavioural economics stories around myopia, hyperbolic discounting, or habituation, then you might be worried about schemes that make people indifferent to working.

Dillow writes:
Which raises the question: why is the campaign for a living wage so much more popular than that for a basic income? I suspect the answer has less to do with technocratic or high-brow ethical considerations than an appeal to reciprocity: the living wage demands that hard workers get a "fair" deal. But I wonder whether such appeals - powerful as they are - are a sufficient basis for policy.
I don't expect that Dillow is wrong about this - reciprocity norms are strong, and intuitions about the deserving and undeserving poor go back an awfully long way. But we can give a technocratic objection to guaranteed basic income schemes: if the guaranteed wage is high enough to make it an attractive alternative to working, which it has to do to give workers the kind of bargaining power that Dillow is looking for, then it also risks enticing those who should be entering the job market at low wages and working their way up to instead lock themselves into a permanently lower path.

I'm not opposed to moves to shift from the current welfare framework to a GAI via a negative income tax, combined with lump-sum transfers for specific hardships like severe disability. But I worry about the kinds of things that Senior and Mill worried about rather a while ago.

Here's Andrew Farrant on those debates:
Poor relief and slavery: Senior's conjecture?

As noted earlier, Nassau Senior argued that slavery and socialism had much in common. Similarly, Senior, in an 1841 article appearing in the Edinburgh Review, had scathingly argued that the perverse incentives allegedly inherent to the English Poor Laws (e.g., the provision of outdoor relief to ostensibly indigent but able-bodied laborers) had done much to reduce "able-bodied paupers" to de facto slavery (Senior 1865 [1841]: 45-115); as Senior puts it, the poor laws had supposedly attempted to provide the able-bodied laborer with:
[A] security incompatible with his freedom; to oprovide for him and his family a comfortable subsistence at his own home [outdoor relief], whatever were his conduct, and whatever were the value of his labour ... [This] attempt succeeded in what have been called the pauperized districts, and placed the labourer in the condition, physically and morally, of a slave; - confined to his parish, maintained according to his wants, not to the value of his services, restrained from misconduct by no fear of loss, and therefore stimulated to action and industry by no hope of reward.
(Senior 1865 [1841]: 115, emphasis added)28
Accordingly, outdoor relief had supposedly occasioned various incentive-incompatibilities - supposedly "fatally relaxing the springs of industry and the restraints of prudence" (Mill 1965: 360) - prior to 1834.28 Accordingly, while the desirability of poor law reform was supposedly apparent to all and sundry, the "Commissioners of Inquiry had reported that it was not expedient, or even practicable ... [to [exclude from relief the able-bodied labourer who professed to be unable to earn wages adequate to the support of his family" (Senior 1865 [1841]:91; emphasis added).30 Consequently, an incentive-compatible poor law would supposedly guarantee that only the truly indigent received able-bodied relief. As Senior notes, incentive-compatible poor relief would automatically "test .. the truth of ... [the able-bodied applicant's] representations" (ibid.; emphasis added). The test favored by Senior was relatively simple: make the receipt of poor relief markedly "less eligible than independent labour" per se (ibid.); as Senior explains, this was easily done by conjoining the receipt of poor relief to a "condition which no man not in real want would accept, or would submit to when that want had ceased" (ibid.: 91; emphasis added). Consequently, the 1834 New Poor Law stipulated that any applicant for able-bodied relief
enter a workhouse ... supported there by a diet ample indeed in quantity, but from which the stimulants which habit had endeared to him were excluded - should be subjected to habits of cleanliness and order - should be separated from his former associates, and should be debarred from his former amusements.
(ibid.: 93)31
Accordingly, indoor relief - the workhouse test per se - was allegedly incentive-compatible: only the truly indigent would voluntarily accept workhouse discipline. As Senior explained, whenever any able-bodied, and self-professedly, indigent laborer readily "accepted these terms, that acceptance [automatically] tested the reality of his wants (ibid.: 91; emphasis added).

As Mill, readily subscribing to Senior's logic, later explained, the wholly "pauperized districts ... have been dispauperized by adopting strict rules of poor law administration" (Mill 1965: 961; emphasis added.)
Read Farrant's whole treatment of the debates around incentives and the old British poor laws.

I don't think we can or should return to the poor laws mandating indoor relief. But the incentive problems laid out by Senior and Mill sure have not changed in the last couple of centuries. At the margin, consideration of these issues should move more welfare transfers from cash for poor people to subsidies for early childhood care, and suggests that any GAI that approaches a living wage would not achieve the appropriate separating equilibrium.