30 Jan 2017

An Apparent Contradiction in Economic Analysis of Social Security

Economics 27 Comments

I am working on an essay on Social Security reform, and I ran into what at first seemed a contradiction. I actually don’t think there really IS a contradiction, but since I am having fun thinking through it, I wanted to share with the other geeks reading this blog.

So right now, a salaried employee has 6.2% of his gross pay taken out for OASDI, while the employer pays an extra 6.2%. (It caps out after a threshold of gross pay, which was $118,500 in 2016.)

Suppose the government allows employees to opt out of this particular payroll tax. What happens to the take-home pay of an employee who exercises this option? I have two different answers, both of which seem to flow from textbook analysis:

(1) In the original equilibrium, the market was competitive and so the employee was getting paid his marginal product. The employer took the 6.2% employer “contribution” to Social Security into account when hiring. Now that the government is removing that implicit fee, the employer will still end up paying the total marginal product to the employee, but now it will be in the form of higher gross wages. Thus the employee will pocket the entire 12.4% of the tax reduction.

(2) As with any case of tax incidence analysis, to figure out how a tax is “borne” by the buyer and seller, what matters is NOT the statutory incidence, but the relative elasticities of supply and demand. By removing a tax on labor, both parties will tend to benefit. The only way the gain would accrue entirely to the employee is if the supply of labor were perfectly inelastic and/or the demand for labor were perfectly elastic, which we have no reason to suppose. (In case you think I got those conditions backwards: Note that if lifting the tax is to help only the employee, that means imposing the tax must only hurt the employee.)

So which answer is right? And why did the wrong one, go wrong?

P.S. It’s actually not right to treat the Social Security payroll deduction as a tax, because it is (loosely) tied to a future payment from the government. It’s more correct to view it as a forced investment in a mediocre annuity program, but even this isn’t exactly right because the withholding/benefit rules are so screwy. But for the purposes of this post, don’t worry about this complication; just treat it like a 12.4% tax on wages that is being lifted.

27 Responses to “An Apparent Contradiction in Economic Analysis of Social Security”

  1. Scott says:

    This is a great question. I think it is 2, but I don’t have a great reason why.

    Also, your PS is exactly what I was thinking as I was reading — you actually ‘get’ something, so it isn’t totally a tax. Presumably the employee discounts the value of the SS he is getting by having a job and adds it to his salary?

    • Jan Masek says:

      Well, don’t you “get something” for any tax? Like free education etc?

      • Scott says:

        Well, okay, but SS is not quite the same. If you don’t pay into SS a certain number of ‘credits’, you don’t receive any benefits, and also the total benefit you receive is determined by how much you paid in. And some professions do not pay into SS at all (teachers, clergy, some government workers) and don’t receive anything.

        To be able to claim most tax benefits (schools, etc) does not actually turn on whether you paid in or not. This is a perennial issue between Republicans and Democrats, and why a large slice of republicans support SS and Medicare but not other forms of welfare — they don’t see it as welfare.

  2. Major-Freedom says:

    Haven’t worked through the answer yet, but one thing I thought to mention is what effect, if any, the reduction of OASDI payments to people will have on the supply of labor (from, for example, people going to work who otherwise would have sought taxpayer financed income).

    This would reduce nominal wages, but increase real wages.

  3. Scott says:

    Ok ok, I’ve got it!

    Neither one ‘goes wrong’. It is just that the assumption of 1 assumes a static labor supply and demand. The second does not.

    I guess you could say that’s where 1 ‘goes wrong,’ if you really wanted. But I probably wouldn’t think of it that way… both are useful ways of thinking about it.

  4. Scott says:

    OK — one more just for fun:

    how about a #3 — the employer gets almost the entire benefit. Clearly, if the employee accepts the current salary, this is the best he can get. If he gets one red cent more out of the deal, obviously he’ll accept. The employer only has to offer him a penny.

    • Tel says:

      But in the same market another different employer might offer two pennies.

      If there’s one big employer (Monopsony) then the marketplace is not competitive.

      • Scott says:

        I was trying to stretch/constrain it in the way Bob constrains #1.

        But yeah, that sounds right. Just because no employer will offer more with the tax does not necessarily mean that no employer will offer more if the tax is removed.

        I was trying to use the argument you often see for why companies don’t just tack their taxes onto prices — if they could do that before the tax, then they would. This is a way you sometimes see people assert an extreme form of ‘consumer sovereignty.’

        Seems like there should be some pseudo-argument that constrains things to give a similar result in this case. “If the employee could get more money for his labor, he would.”

  5. Silas Barta says:

    I think 2) is correct and 1) is, as suggested, ignoring the impact on the overall labor supply, which may be to draw in more marginal workers, bidding down effective wages, and making net wages lower than you would get from subtracting off the tax.

    • Capt. J Parker says:

      I think you are exactly right as far as you go. Lifting the tax will draw in more marginal workers that may bid the labor price down BUT, it will also draw in more marginal consumers of labor which will bid the labor price up. At the end of the day the new labor price is all about the relative price elasticities of the supply and demand for labor.

  6. khodge says:

    I don’t like binary answers.
    Plausible alternatives may include: Benefits that accrue to the employer as much as to the employee, such as training that benefits the employer without necessarily offering transferable skills; cash intensive changes to the compensation structure; profit sharing programs that allow future compensation and mitigate current cash-flow problems.

  7. RL Styne says:

    Isn’t #1 just another way of stating the restrictive conditions in #2 (i.e. inelastic supply or elastic demand)?

  8. Andrew_FL says:

    If I have a pre-existing labor contract with an employer and then the tax is eliminated, the statutory incidence actually should matter because unless I renegotiate the labor contract, as I understand how the tax works I will only get the 6.2% which may be more or less than my original tax burden. 1 seems to implicitly assume I can renegotiate for my before tax wages to be increased by the amount of the employer contribution which seems unlikely.

  9. Capt. J Parker says:

    It’s 2. The tax as structured shifts both the supply and demand curves for labor to the left. When the tax is lifted the labor market will assume a new equilibrium market price and quantity demanded for labor. The new equilibrium wage will depend on the elasticities of both supply and demand for labor. If the elasticities of supply and demand are identical then the benefit of lifting the tax is split equally between the employer and employee. Number 1 incorrectly assumes that labor market as a whole is unchanged when the tax is lifted.

    • Bob Murphy says:

      Yes, others were saying this too, but just to confirm my own thoughts, I think Capt J Parker got it. So it’s true in (1) that w=MPL, but MPL might be lower in new equilibrium.

      What’s also interesting is that even if a particular individual doesn’t opt out, his MP will fall. So it’s not him opting out, it’s the opt-out power being given to everybody that does it.

      • Capt. J Parker says:

        Dr. Murphy said “So it’s not him opting out, it’s the opt-out power being given to everybody that does it.” I’m not sure this statement makes all that much sense for this reason: If, as per the premise of the puzzle, the tax is just a tax with no benefit to employer or employee from paying it then all employees will opt out. If they don’t it would be a big violation of the “no money is ever left on the table” principle. If given the ability to opt out everyone does in fact opt out then there is no distinction between opting out yourself and others having the power to opt out.

        If you really want to answer the question of what happens when some workers opt out and others do not and what that means for w=MPL then to need to add in to the problem statement an economic reason why some do not opt out and crunch through that more complicated problem. I can imagine things getting really messy trying to deal with some kind of segmented labor market.

      • Silas Barta says:

        Don’t know if this helps, but you can think of it like a transition between “workers must be paid in donuts” vs “workers may be paid in cash now” — to buy the same labor, you have to pay a lot more donuts than the equivalent cash value. So after such a transition you’d find a lower value being paid to workers because workers prefer $8 of cash to $10 of donuts.

        (I will hunt down anyone who makes dollars-to-donuts puns.)

        This scenario is basically the same as that, except that it’s a transition between “workers must receive 6.2% of their compensation as purchase of Social Security” to “… 0% of their compensation”.

        • Bob Murphy says:

          Yep good thought Silas, though for this particular post I’m trying to isolate the tax per se. But yes you’re right, it’s not really a tax, it’s a regulation on the percentage composition of compensation.

  10. Tel says:

    When you say, “In the original equilibrium, the market was competitive …” the implication is there are many employers for each employee to choose from, and all of them offer the opportunity to opt-out of OASDI.

    In that case, we would expect that no single employer can significantly alter the market price by throttling demand for labour, they are simply price takers. This in turn would imply the subjective demand curve is locally horizontal in the vicinity of equilibrium (from the perspective of any particular employer).

    NOTE: This does not prove that global demand curve is horizontal, because there’s a big difference between the partial derivative for the single employer (what happens if I employ fewer people and everyone else stays the same) as compared with the whole market derivative (what happens if everyone employs fewer people). As Scott says above, should the global supply change then this will move the price (e.g. if there are people sitting on the sidelines not working at all, but then the OASDI opt-out makes them interested in working, so the total supply of labour increases). We would expect that any additional incentive to work would also increase the number of people interested in working (well, I would expect that).

    • Tel says:

      I’m not feeling myself today…

      Stupid web browser loaded a different ID, and I wasn’t paying attention so I got tricked by it. The penalty of getting complacent with automatic systems.

  11. baconbacon says:

    Bob, I think you make a small mistake with #1. Say you produce exactly $5 an hour for your employer, you employer is totally indifferent to hiring you at $5 an hour or not hiring you at all, as his net is the same (you produce $5 and hour and make $5 an hour so his net is $0, or you produce $0 an hour and are paid $0 an hour so his net is $0 an hour when he doesn’t hire you). The real representation is a limit function where employers will pay up to, but not including, $5 an hour for a $5 an hour employee, so an employee never quite makes their marginal product.

    For #2 you have ignored capital structure. Start a widget factory that can produce up to 100 widgets a day requiring 100 pounds of steel per day, what is the relevant marginal factor? If marginal cost of steel is $10.00 per pound then I will happily pay $10.00 per pound for the 99th pound of steal if I can sell my 99th widget for $10.01+, but I will not buy the 101st pound of steel for $10.00 as that exceeds my capacity, and a second factory won’t be built unless I believe that I can secure a supply of steel at $X per pound and I can sell those Y widgets for $X+Z each where Y*Z is > the costs of building the new factory.

    Now a 10% tax on steel is introduced

    1. If this makes a proposed new factory unprofitable, who “pays” the tax on that steel? Technically the answer is “no one” because the steel is never purchased and widgets never produced and sold, so the tax is never collected. On the other hand consumers lose out on their surplus, the factory owner misses out on profit from selling them and the steel producers miss out on the sale of more steel, what gives?

    What gives is that we have shifted the supply curve, and because we have capital costs (the startup of the new factory) the overall loss is greater than the marginal tax rate, and so both the seller of the taxed good and the buyer(s) of the taxed goods can have losses even with one side fully “absorbing” the costs of the tax.

    This is the same mistake that Marx makes in his labor theory of value, so you have that going for you, which is nice.

    • Bob Murphy says:

      Baconbacon on your #2:

      It is standard in this type of analysis to focus on the actual (after-tax) price, rather than looking at consumer and producer surplus. So if *that’s* the essence of your critique, fair enough, but I wouldn’t say it was a mistake, but rather that I was showing how two staples of textbook theory seemed to contradict on this.

      Also, it has nothing to do with capital structure (assuming I’ve understood your critique). If someone tells jokes in the square for $5 from each person in the audience, and then the government imposes a $1000 tax on the seller, no revenue is collected. So does that mean no harm done? Of course not, because loss of producer and consumer surplus. But no capital is involved.

      • baconbacon says:

        @ Bob,

        I was trying to take a shortcut to make it shorter, so now it has to be longer, if only there was a lesson that I could learn there.

        The capital structure comes in the example when you consider how to make the new factory profitable. If it is profitable when you can produce and sell at least 80 widgets a day with a specific profit margin then a tax rate that would drop the production from 80 down to 79 per day would prevent not 1 widget from production, but 80 down to zero. Because capital doesn’t scale in a linear fashion (i.e. you can’t just decease the productive capability of the new factory to 79 at the new cost of steel), the net loss is greater than is implied by the increase in marginal cost of the steel.

        The trouble is that every problem has capital in it. Unless your joke teller literally lives in the middle of the square rent free and never has to travel away from that point to acquire goods and serves then he has capital costs which he has to overcome.

        • Baconbacon says:

          To clarify the marginal product entirely going (or almost entirely) to the worker is correct in a world with with zero, or infinite, capital. This is the same outcome as Marx got because he assumed a linear return to capital which only happens under those conditions. By stripping out investment/capital and than applying marginal analysis you get the labor theory of value.

  12. Get Real says:

    The “contribution” to the SS program is a tax. There are no assets in the Trust Fund because Congress has “borrowed” all the “contributions” to fund the annual budget, leaving IOU’s (promissory notes). Those notes are not enforceable by the contributors because there exists no legal mechanism for doing so. The current payments to beneficiaries are made out of the current budget, so the beneficiaries (prior contributors) are being paid out of “contributions” from the present “contributors”. This a Ponzi scheme, which is a criminal operation if done by someone that is not the government.

    Contributions to the SS program are not voluntary; non-volunteers are prosecuted for tax evasion, proving that the “contribution” is actually a tax. A legitimate insurance contract is voluntary and is enforceable against the issuer of the policy. Also, the fact that SSA pays benefits to non-contributors, like illegal aliens and “refugees”, is defacto proof that the real “contributors” are being dunned (taxed) to finance a welfare scheme to benefit criminals.

    Employee pensions are voluntary only to the extent that employment with a given employer is voluntary; but all employees are compelled to participate in “contributing” to the pension fund. Regrettably, in recent times, those funds have gone unfunded by the employers; and the courts have allowed the employers to renege on their pension obligations that were parts of employment contracts. In those cases, the employer,s which include some government entities, have stolen the pension assets from the employees.

    SS is a fraud perpetrated on victims who are powerless to protect themselves against it. And please spare me the canard that elections can change Congress and end the crime. If that were true, SS would have ended generations ago.

    • Bob Murphy says:

      Yes, don’t worry, in the thing I’m writing, I go through the stuff about the Trust Fund and how it actually works. The context of the piece is that the funding gap is so big that they are going to have to do something soon, and I’m trying to come up with things to minimize the pain.

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