I'm confused about a decision theory problem related to taxes.

If I get a large tax refund, that means I over-paid taxes earlier in the year. So it's better overall if I get no refund.

But I already know how much money I currently have, and whether I overpaid my taxes in the past doesn't change that. If I get a large refund, I will have strictly more money than if I hadn't gotten a refund. So it's better if I get a refund.

These arguments can't both be correct. I suspect the second one is wrong, and it's preferable to get no refund, but it's not clear to me why.

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Holding constant the total amount of taxes you pay, it is better not to get a refund. This is the perspective you should take at the beginning of the year. 

Holding constant the amount of taxes you have already paid, it is better to get a refund. This is the perspective you should take at the end of the year. 

My attempt to answer my own question:

The preference to get/not get a refund is a derived preference. My true preferences are to both owe and pay as little tax as possible. If I am in a situation where I can change how much tax I pay, but not how much I owe (by setting my withholding), then by maximizing my preferences I happen to minimize my refund. And if I can change how much I owe (e.g., by taking different deductions), but not how much I pay, then by maximizing my preferences I happen to maximize my refund.

This is a silly thing to have much of a preference over.  It matters very little in most cases, and it's at least partly in your control (mostly in your control, in the cases that matter).

Or maybe you're asking for a recommendation for an plan (in which case framing it as a preference is confusing).  For me, the emotional and logistics cost of under-withholding and owing money when filing is much higher than the very small amount of interest foregone by over-withholding and getting a refund.  That may or may not describe you.

Don't forget that (in the US, at least) there is a fine for owing too much tax at filing time, while there's no penalty for having paid too much except for opportunity costs. Given the extremely low interest rates currently, the risk is not symmetrical.

I think there are several factors to consider before you can answer for your self. 

First, discount rates. What is your discount rate for future money? If that is high then clearly getting the refund is not optimal for you and you'd be better off setting deductions such that you don't get much of a refund (or even perhaps owe a small amount). However, if your discount is 0 then you don't care if you get the money now or sometime in the future. 

The implication here seems to be that getting the refund is at best no better than not getting the refund. One might take a further step to say over the course of a year various things can come up where having a bit more cash would help so, risk adjusted, the refund is the second best choice for you.

The flip side might relate to personal financial discipline and spending habits. If you need to save (say for larger ticket item things or for placing in a savings/investment account) but struggle to achieve that the refund may well be better. It becomes something of a forced savings strategy. Money you never see is much easier to save than money you hold in you hand.

I don't have any formal math for you, but my answer is that trying to not get a refund is a planning question that involves predicting the coming year, whereas trying to maximize your refund is a strategic question about filing your taxes after the year happened. In other words, tax owed or refunded at filing time is a measurement of prediction error about your expectations for the prior year.

At any given time, I can make tax withholding decisions (or estimated tax payments for the self-employed) that I expect will mean I pay the exact right amount in withheld taxes. However, between now and the end of the tax year, lots of things can happen. My income can change, the tax rates can change, I can buy or sell a house or car and both my deductions and tax obligations can change, I could get married or otherwise change my filing status, and so on. There are enough variables outside my direct control that I should not expect to always get this right.

When I file, I have all the information. I know exactly what happened, where reality differed from my predictions. Yes, there may be things I can do even then in how I file that might legally change the outcome, but in general that's a question of skill in reading legalese and filling out forms.

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