NYU Tax Policy Colloquium, week 12: Abdou Nidaiye's Redistribution with Performance Pay

Yesterday at the colloquium, we discussed Redistribution With Performance Pay with Abou Ndiaye, a new NYU colleague of ours at Stern. This was a technically challenging paper for our group, not to mention its convenors, but rewarding to discuss as it relates to matters of broader intellectual interest.

The paper brings together 2 overlapping literatures, both dealing with "insurance" broadly defined. The first is the optimal income tax (OIT) literature, while the second is in labor economics and deals with performance pay.

We're in the insurance realm whenever there are choices between more fixed & more variable returns, with risk aversion giving people some preference for the former (for which they might be willing to pay in expected payoff terms, up to a point), but where problems such as moral hazard and adverse selection might 

Optimal income tax - Here the idea is to insure against ability risk, where "ability" is a stand-in for wage rate or potential earnings, rather than having any of the word's ordinary English language valence. One might also add in insuring against the risks associated with one's having under-diversified human capital (since specialization is pretty much mandatory in the labor market).

In the classic model, the government can't observe ability, but only income, which is the joint product of ability and effort (which also can't be observed). A private firm can't provide ability insurance due to adverse selection - only those with private negative information about their earnings prospects would enroll. The government can in principle solve that problem, absent significant entry and exit based on its fiscal rules, but it still has to deal with moral hazard, i.e., working less by reason of the tax. This doesn't prevent it from offering the insurance via Mirrlees' labor income tax (which ignores both investment and saving, and hence capital income, since it is a one-period model), but the government has to address moral hazard by including a significant co-pay (i.e., 1 minus the marginal tax rate).

Principal-agent in the workplace - If you're self-employed and have some sort of a business, then you're at full risk, the tax system et al aside, with regard to how much you end up earning. But suppose you work for a firm. In Coase's theory of the firm, this may reflect some sort of tradeoff in which using contracts to create command hierarchies in lieu of ongoing, flexible market interactions has a net payoff, perhaps by reason of its constraining strategic behavior in midstream between parties engaged in joint production. But this can lead to principal-agent problems, where the agent (the employee) has reason to shirk the provision of maximum effort.

Suppose the employee has purely fixed compensation. This can make the shirking problem especially bad. The firm can respond by offering performance-based compensation, where the employee does better if, e.g., sales or profits are high than if they are low. But suppose that, while effort is hard for the employer to observe, the performance output reflects both the unobserved effort level and equally unobserved good or bad luck. Then, if the employee is risk-averse, the employer has reason to offer insurance in the form of a wage that is partly performance-based and partly fixed. Just as in the public OIT setting, we have a tradeoff here between insurance value and moral hazard.

Suppose further that the employer can observe ability although not effort. Indeed, to make it simpler still, suppose for now that all of the relevant employees have the same level of ability.

To create a handy toy example, suppose that the firm's principal-agent insurance problem is optimized by telling the firm's two employees, A and B, that they will receive $80 in the event of a bad outcome, and $120 in the event of a good outcome. As it happens, A earns $80 while B earns $120.

But now, in rides the Mirrleasean income tax. Despite its being totally unneeded here - since A and B have the same ability, and also since the firm is already optimizing the tradeoff between insurance value and moral hazard - it uses a 50% income tax to fund a $50 demogrant.

Therefore, A's $80 pre-tax and transfer return is reduced to $40 by the tax, then increased to $90 by the demogrant.

B's $120 pre-tax and transfer return is reduced to $60 by the tax, then increased to $110 by the demogrant.

Given the assumptions about optimization, there is now too much insurance, given the tradeoff between insurance value and the costs of moral hazard. But not too worry, a familiar adjustment that the paper calls "crowd-out" may ride to the rescue here.

Suppose the employer now shifts the pretax payouts to $60 / $140. As again, suppose A ends up with $60 before taxes and transfers, while B ends up with $140. Now things play out as follows:

A's $60 pre-tax and transfer return is reduced to $30 by the tax, then increased to $80 by the demogrant.

B's $140 pre-tax and transfer return is reduced to $70 by the tax, then increased to $120 by the demogrant.

The firm has therefore re-optimized, undoing the harm done by the government's unneeded insurance. It's unneeded in the example because (a) there is no adverse selection issue since everyone has the same ability (known to the firm), and (b) the government has no advantages in addressing moral hazard - which, in a real world example, it might! (E.g., suppose it has discovery powers. Or, in terms of the underlying employee risk aversion, suppose it more knew about people's household circumstances, e.g., other types of income and wealth, family members, etc., that enabled it to better gauge who is likely to want how much insurance, assuming strategic behavior and transaction costs impeded firm-worker negotiations).

But actually the government has made things worse here, once we expand what we are looking at a bit. It has reduced work incentives, e.g., because A and B would still get demogrants if they quit.

The conclusion that the government should just butt out is of course not at all robust, once one pushes the hypothetical back in the direction of representing the real world. After all, ability variation, and the consequent need for ability insurance, is key to the whole OIT model. Plus, the firm can only insure against a limited range of outcome resolutions - say, high vs. low sales within its sector based on common chance factors within its experience. The risk that the firm's industry will either collapse or go ballistic in a good way may lie outside its insurance capacity, giving value to the government's capacity to ensure against human capital under-diversification risk. And there's also the issue of self-employed people who work outside of firms, unless they can find the same insurance without actually joining a firm in which they are subject to hierarchical command in cases where that's not productively optimal.

Within the model, however, we may be glad about "crowding out" - i.e., the firm's increasing pre-tax variation so as to get back to the right place despite the locally unneeded effects of the government's offering broader social insurance. One might need to know more, however, in order to judge whether the crowd-out has, say, such undesirable collateral consequences as 

This is all completely standard. It's the paper's starting point, rather than something it's asserting or testing. But one motivation for the paper is that, in the performance pay literature, although I'm not personally well-acquainted with it, there is thought to be a bit of a mystery in the form of our not observing crowd-out adjustments when tax rates change. E.g., although this alone would not be conclusive, in the last few decades we have simultaneously seen a decline in tax progressivity and an increase in at least nominally performance-based pay for high-wage employees. (I say "nominally" because, for example, CEO bonuses paid by the captive boards of publicly traded companies may play games in order to mislabel very high pay as being more performance-based than it actually is.)

The paper's main contribution is to discuss what it calls crowd-in, and which in its model pretty much full offsets crowd-out. We get crowd-in if the presence of the income tax causes the optimal deal between firms and employees to include more fixed pay, and less performance pay, than would otherwise have been example. Here's the toy illustration, just to show what's going on.

Again, recall that crowd-out changed the pre-tax and transfer compensation package from 80-120 to 60-140, so that it would still be 80-120 after-tax (leaving aside that, if employee effort declined, the wages presumably would too). So now, treating the crowd-out as Stage 1, there is a Stage 2 problem. Because of the presence of the tax, the optimal deal between the firm and the workers has shifted towards having MORE fixed pay and less performance pay than in the absence of the tax and demogrant.

Suppose that the optimal deal is now 90-110. While crowd-out, considered in isolation, would have shifted the pre-tax deal from 80-120, crowd-in shifts it all the way back to 80-120. So now we get the following, all-in so far as both sets of changes are concerned:

A's $80 pre-tax and transfer return is reduced to $40 by the tax, then increased to $90 by the demogrant.

B's $120 pre-tax and transfer return is reduced to $60 by the tax, then increased to $110 by the demogrant.

But, compared to the discussion earlier, this is now optimal, given the tax.

Again, this simple depiction of responses to the tax ignores the key idea here that the tax would lead to reduced labor supply, hence the actual deal would have to be for reduced dollar amounts. But it treats crowd-out and crowd-in as precisely offsetting - the model less exuberantly asserts that they will be largely or roughly offsetting - and hence might be used to explain empirical findings that fail to discern any crowd-out occurring when tax rates decline for the folks who are getting performance pay.

What would be the intuitive explanation for the crowd-in adjustment? The paper's current draft may not make this as clear as subsequent drafts no doubt will. But the primary explanation appears to be that, with labor effort being suppressed in all dimensions (and with substitution effects empirically outweighing income effects that might push the other way), there is simply less point to using performance pay to goose up employee effort. Less of that, and more fixed pay in response to employee risk aversion, turns out to characterize the optimal deal.

A secondary explanation, albeit not similarly relied on by the paper, might be the income effect of workers' having less $$ by reason of working less, and thereby objecting more to risk that they would have considered fine in the presence of a larger cushion. But that effect might be mitigated anyway by the use of the tax revenues, e.g., in the standard OIT set-up to fund demogrants.

If most readers of this blog are more attuned to prose than math (as I myself am), they may find the paper challenging to read. But here's hoping that this rendition of it is useful, since the ideas are worth considering and it's good to bridge the space between both the OIT and performance pay literatures, and people in different sub-fields within tax policy / public economics.