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On Balance: How Irrationality Affects the Value of Cash Transfers
04/06/2021

By Dan Acland, University of California Berkeley

Financial transfers from taxpayers to program recipients (such as Temporary Assistance to Needy Families, or TANF, in the US), are treated as having no effect on net benefits in benefit cost analysis, because, in dollar terms, the benefit they generate for recipients is exactly offset by the cost to taxpayers.  But if poverty has the effect of reducing the rationality of recipients relative to taxpayers, and if getting out of poverty increases it, then transfers may actually generate a non-zero net benefit, which could be positive or negative. 
The basic argument goes like this. If the recipient makes allocation decisions that are less rational than the taxpayer's, then the recipient will receive less benefit than the taxpayer loses, because the recipient will allocate the money less efficiently than the taxpayer would have. The recipient's choices will fall short of fulfilling their true, or rational preferences than the taxpayer's. Thus, the transfer generates a negative net benefit. Conversely, if the transfer has the effect of lifting the recipient out of poverty enough to increase their rationality to the same level as the taxpayer, then not only will they allocate the transfer as efficiently as the taxpayer, but they will also reallocate their pre-transfer budget more efficiently than before, so the transfer will generate a positive net benefit. If we had enough information about the preferences and rationality of taxpayers and recipients, and about the effect of transfers on rationality, we could compute the negative or positive net benefit of transfers, and include it in benefit cost analysis.
 
For example, consider the case of present bias, which means placing greater weight on outcomes in the immediate present than on outcomes in all future periods. This is different from the standard model of exponential discounting, in which each period is discounted relative to the one before. Present bias is the phenomenon of additionally discounting all future periods relative to the present. Present bias is a form of irrationality. In the technical sense, it is irrational because it causes failures of transitivity, or "preference reversals." On Friday I prefer to eat some cake on Saturday and some on Sunday, but on Saturday I eat all the cake. Present bias is also irrational in the common sense of the word, because it causes individuals to make choices that make them worse off in their own estimation, such as eating unhealthy food or failing to invest in education. We all do this. The important question is whether individuals do it more when they are poor.
 
There is some evidence that poverty does affect rationality, which I review in my paper. The most relevant and compelling comes from a growing literature on the phenomenon of scarcity. Not having enough money (or time, or any other resource) creates a sense of scarcity that has been shown to affect cognitive capacity and self-control, both of which are essential to decision making in many consequential areas of life. The argument is not that the poor are irrational and that their irrationality causes their poverty, but rather that poverty causes irrationality. The direction of causality is crucially important to me, first because I wish to take no position on the debate about whether or not the poor are responsible for their poverty, and second, because if irrationality caused poverty, and not the other way around, there would be no reason to think that transfers would increase rationality, and thus no mechanism by which transfers could generate a positive net benefit.
 
My argument would be more or less academic if there weren't some way to compute the net benefit generated by any particular cash transfer. In my paper I make a first attempt at doing so. First I write down a mathematical model of present-biased preferences. There are two goods, one of which has immediate benefits and long-term costs, the other of which has only immediate benefits. I model a taxpayer and a recipient with identical preferences, except for the proportion by which they discount the future cost of the first good. I calibrate the model using parameter estimates that approximate the case of ultra-processed foods, and discount factors that reflect existing literature on discounting and scarcity. I use computational methods of utility maximization to compute the bundles of goods that each individual will consume, both before and after the transfer, which is to say, the bundles that maximize their irrational utility functions. Then I use expenditure minimization to compute the minimum budgets that would achieve the same level of utility for the rational self as the irrational bundles do for the irrational self. These expenditure-minimizing budgets are the dollar values that the rational self places on the bundles of goods chosen by the irrational self. 
 
Using these numbers I am able to compute, in dollars, the true cost of the transfer to the taxpayer (which is less than the dollar value of the transfer due to present bias), and the true benefit of the transfer to the recipient (which is less than the cost to the taxpayer if the transfer does not significantly increase the recipient's rationality, and more than the cost to the taxpayer if it significantly increases the recipient's rationality). The difference between the two is the net benefit created by the transfer. In the case of present bias, if the transfer doesn't significantly increase the weight the recipient places on the future, the net benefit of the transfer will be negative, because the recipients allocation of the transfer will be less efficient than the taxpayer's. If the transfer does significantly increases the weight the recipient places on the future, the net benefit of the transfer will be positive, because the recipient will allocate both the transfer and their pre-transfer budget more efficiently than they would have, and will thus wind up with a benefit from the transfer greater than the cost to the taxpayer, and potentially greater than the dollar value of the transfer itself. 
 
Using plausible parameter estimates, I estimate the net benefits of the combined benefits of federal cash-transfer programs for a single-member household and find that there is a plausible range of present bias in which the transfers generate a net benefit greater than the excess burden of taxation. The benefit-cost ratio reaches unity when the beta parameter in the standard model of quasi-hyperbolic discounting under extreme poverty is approximately 0.4 and climbs to approximately two for a value of 0.3. These are low values but not out of the range of what is plausible. If the model included additional forms of irrationality, or additional goods affected by irrationality, the positive impact would be stronger. I explore the results for different parameter values. The net benefit primarily depends on three things: how poor the recipient was before the transfer, how much more present-biased the recipient was than the taxpayer before the transfer, and how much the transfer increases the rationality of the recipient. Not surprisingly, holding other things constant, the benefit is greater the more present-biased recipients are pre-transfer, and the more the transfer increases the rationality of the recipient. But, somewhat surprisingly, holding other things constant, greater pre-transfer poverty reduces the net benefit, because it reduces the size of the pre-transfer budget that the recipient reallocates more efficiently as a result of the transfer. 
 
My results have a couple of interesting policy implications. The first is that, under any plausible combination of parameter estimates, there is no way for a well-intentioned paternalist to make recipients better off through carefully targeted in-kind transfers than they would be with cash, regardless of the effect of transfers on rationality. This is because it is almost guaranteed that a recipient of an in-kind transfer would be able to reallocate their pre-transfer budget in such a way as to achieve their irrationally preferred bundle, even when accounting for the flypaper effect. Second, since there are plausible parameter values under which transfers increase rationality enough to offset the excess burden of taxation, there may be opportunities for public policy to untie the Gordian knot of efficiency and equity and increase both at the same time.
 
Our understanding of the effect of poverty on rationality, and our ability to model decision making under irrationality (and to parameterize our models) are not at a point where it would seem prudent to start using my methodology in practice in regulatory impact assessment. But I do feel that it is important to start thinking about the issue, and that my work expands the scope of to the nascent literature on adjusting values in benefit cost analysis to account for the effect of irrationality. The obvious next step is further research on the effect of poverty on rationality, which needs to establish effects, but also needs to generate parameter estimates. Models of most of the relevant forms of irrationality exist, but are typically highly simplified, as their primary goal has been to test hypotheses and generate insights, rather than to provide concrete policy predictions. It isn’t clear whether further refinement of the models would improve the quality of the results enough to warrant the endeavor, but development of a unified model that captures all of the relevant forms of irrationality will be necessary.
 

This post summarizes an article in an upcoming issue of the Journal of Benefit Cost Analysis.
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