Scott Sumner  

How much do government workers cost?

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Tyler Cowen directed me to an interesting question raised in his comment section (by "BC"):

Do federal employees pay income tax on their wages? I know they do nominally, but that tax goes back to their employer, the federal government. So, doesn't that mean that, while their actual salary may be lower than their official nominal salary, they actually don't pay any tax? (NB: this is quite different from a private sector employee whose after-tax salary is less than the pre-tax salary. In that case, the difference between the two does *not* go to the employer, creating a gap between what the employer pays and what the employee receives.)

For example, suppose a private firm and the federal government both value a worker's output at $100k/yr and the tax rate is 20%. The private firm offers the worker $100k and the worker receives $80k after paying taxes. The federal government, however, can offer the worker $125k in nominal salary, *knowing that it will receive $25k back in income tax*. The net result is that the federal government pays $100k and the worker receives $100k after taxes, i.e., the worker earns $100k tax free, $20k more than he or she would earn at the private firm. Another way of seeing this is to note that taxes paid by employees are economically equivalent to taxes paid by employers. So, if employers received rebates for income taxes paid by employees, then the net income tax would be zero. Well, the federal government *does* receive a rebate for all income taxes paid by employees!

Doesn't this mean that taxes are doubly distortive? Not only do they discourage employment by creating a gap between what (private) employers pay and what workers receive -- the usual cited distortion -- they also distort the *composition* of the workforce by allowing the federal government to crowd out other employers.


This is one of those cases where things look very different if you recall the macroeconomic linkages. Let's start by assuming that the government hires the worker away from a comparable private sector job. In that case, the tax paid by the newly hired government worker would be offset by the tax no longer paid on the job he left in the private sector. To make things simple, assume a flat rate tax system. Then total tax revenue is the tax rate times national income. Thus in order for the act of hiring a government worker to result in more total tax revenue, the act of hiring the worker would have to boost national income.

Now we can see that the actual question being asked here is whether or not the act of hiring a government worker causes national income to be higher. Here are some models where that is generally not the case:

1. Monetarism
2. Austrianism
3. Real business cycle theory
4. New Keynesian models with a natural rate of output

And here's one model where it may be the case:

5. Primitive Keynesian models of the sort that were discredited during the 1970s

The wrong way to think about these sorts of issues is to look at accounting relationships at the individual level. "Follow the money". The correct way to approach the problem is to think in terms of aggregates such as "national income". Does government hiring cause national income to rise? If so, then you get more revenue.

PS. In some New Keynesian (and RBC?) models you might get a rise in measured national income, as the government worker would make the country poorer, causing labor supply to increase as a way of preventing an excessively sharp fall in consumption. I'm abstracting from that (second order) issue, which gets into questions about the proper way to measure GDP.


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COMMENTS (10 to date)
Chris writes:

I think the weakness in the argument is that it requires the government to believe and plan around the fact that it’s getting the taxes back to itself. I don’t think this is the case. Each department of a government has its own budget, so in a sense, the argument is not true; the department making salary decisions is not necessarily getting the funds back, at least not the whole portion.

The reasoning implied of the government is also explicitly not the reasoning used by the government in hiring. Government positions offer better benefits as a means of attracting quality labor that would otherwise not want to work with the government due to the downsides that have historically included lack of growth opportunity. The government would offer less if they found they could find and retain quality labor with less. Again, each department has limited funding that is most often decided on from a top down approach completely isolated from the realities of Human Resources and they then do the best they can with that funding.

The reality may be that government employment is reducing the tax base, but I think this gets into the arguments of whether or not that’s okay, and when specifically it is preferable to replace private roles with public ones.

Additionally, if the government hires someone away from a similar position, that similar position will be filled by someone else, and if the private sector has to compete with the government, then the new employee may receive a higher salary. In this case there may still be a net loss in tax base, since one of the two employees now essentially pays taxes to its boss, but there is still someone filling the other position and paying taxes on that wage. Until we hit a scarcity of labor, this will be the case.

If you go further into it, it becomes a form of redistribution. Private taxes are supporting the loss of taxes from the government employee. If overall taxes are regressive, then the government employee is ‘taking’ money from people less well off than themselves; if taxes are progressive, they are taking from those more well off. It’s one thing for people to support the actual value of a government worker (assuming salary is related to value of work performed) and another to support the ‘perk’ of zero taxes as defined in the post. Again, this gets into the discussion of what benefit society gets from the government worker being offered that perk.

I think in the end I’m more arguing around elements of the write up than with it directly, but either way I think the real questions are not as cut and dry as ‘does it impact the national wages’. There are other emergents to the cost benefit analysis and qualitative issues of who should be doing work.

bill writes:

Well said. I also liked your comment over at the MR post.

Is there a similar way to make a similar point about the pending corporate tax rate cut? My mind keeps taking me back to a quote (I think by Milton Friedman) that the cost of government is the spending, not the taxes. It just seems like the unfunded portion of the tax cuts will just mean more borrowing which will crowd out any of the potential investment effects. Conversely, I like the reform aspects on the personal tax side, and it seems like those are being put at risk by the larger corporate tax rate changes.

AbsoluteZero writes:
The wrong way to think about these sorts of issues is to look at accounting relationships at the individual level. "Follow the money". The correct way to approach the problem is to think in terms of aggregates such as "national income".

This is a good example of a general principle. It shows up in many fields. Following the money is procedural thinking. It works but can get complicated quickly for nontrivial problems.

Consider this problem. We have a tournament of elimination matches. Every match will have a winner, there are no draws. Winners move up to the next round. Start with 8 players. How many matches will need to be played to get to the final winner? Most people immediately start thinking procedurally. Pair them up, play 4 matches. Then take the 4 winners, pair them up, play 2 more matches. Then one final match. It's 4+2+1=7 matches.

Now consider the general problem of starting with n players. If n is a power of 2, you can do the pairing and build up a binary tree, then count the number of nodes. It works out to be 1+2+3+...+n/8+n/4+n/2, which sums to n-1. But what if n is not a power of 2? There are standard ways to deal with that, and the result is still n-1. But, as is obvious, it gets complicated very quickly.

Thinking in terms of aggregates, observe that each match produces one winner from 2 players. The number of players is reduced by exactly 1. Start with n, end with 1, the number of matches has to be n-1.

There are many other similar examples not just in theoretical computer science, but in many other fields.

Tyler Cowen writes:

It is more interesting if say you think of the government as bidding for the labor of women who are currently voluntarily unemployed.

Scott Sumner writes:

Chris, You said:

"Until we hit a scarcity of labor, this will be the case."

No, this is the mistake made by the "primitive Keynesians". They wrongly assumed that as long as the economy had slack, there would be no opportunity cost of additional government employment. In fact, one should always assume that there is a "scarcity of labor".

Tyler, I don't think that's right. That's like claiming that more government spending increases the natural rate of employment. That's possible, but extremely unlikely.

There may be some individual women drawn into the labor force by government, but the side effects of expanding government will push away at least as many other workers, due to factors such as higher tax rates (disincentives to work.)

Andy writes:

This argument doesn't make any sense to me.

First of all, government workers are not paid more to cover the costs of taxes. In general, government workers get less pay than private sector equivalents but receive other non-cash benefits instead (ie. job security) to make up the difference - in some cases.

Secondly, compare any government worker to a federal contractor with the same or similar job description. Government contractors are also paid with federal funds and generally receive much higher compensation. (Of course there are always exceptions, but they are very rare.)

Third, I've both been a federal civil servant and I also participated in manning studies which is the process that determines an organization's structure. At no point are federal taxes ever discussed as a factor, it is always about balancing an organization's mission, needs and wants with its current and expected budget. The pay grade is determined by many factors and tax burden is not one of them.

BC (Yes, same one) writes:

Doesn't the income tax lead to deadweight losses and, thus, lower national income? I'm not referring to Keynesian cyclical income, but long-term trend income growth. I probably should not have used the phrase "crowding out", which implies government recruiting employees away from the private sector. Rather, start with a world of no income tax. As the income tax rate is increased, doesn't private employment drop, as does national income, as more people choose leisure and (inefficient) home production? Government employment, however, may not drop because the income tax doesn't actually create a gap between what the government pays and what the worker receives (or so I'm hypothesizing). Hence, no deadweight loss (other than the loss that already existed with zero nominal income tax due to possible government mishiring). So, I guess my question is whether the income tax disincents government employment in the same way as private employment?

If the tax rate were close to 100%, say 99%, wouldn't the end result be that only the government would hire employees? The government could offer an employee $10M in nominal pre-tax salary, receive 9.9M income tax, and thus pay the employee only $100k in net after-tax income. No private firm could afford to hire employees because private firms do not receive the income tax. Is your claim that the government wouldn't be able to afford to hire employees either?

Aside: there could also be a second-order effect too where, as the tax rate rises and private employment drops, government output becomes more valuable (due to lack of private output), so the government actually hires more workers. That would be "crowding out" in a sense.

Chris writes:

Scott,

Theoretically it feels like the added tax on the private worker will be offset by the increase in salary caused by the competitive force of the government’s higher income for the same work. In the end, the tax wouldn’t be felt in income taxes, but may be felt by corporations or in higher prices. So, possibly we feel it as inflation, making our hypothetical tax free government job, in essence, a federal consumption tax.

In general though, as someone else pointed out, the government tends to pay market value for employees and uses benefits as incentives, however I would guess they are able to offer those benefits more efficiently than the private sector due to economies of scale and a lack of profit incentives.

Carl M Case writes:

There is an unmentioned elephant in the room.
Consider all of the regulations and red tape and economically useless activity that each bureaucrat serves in attempting to control individual action and the economy.

Scott Sumner writes:

BC, You asked:

"Is your claim that the government wouldn't be able to afford to hire employees either?"

Yes, where would they get the money?

Chris, You lost me somewhere. Exactly what are you claiming?

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