# Towards auto-stabilizing tax rates

People talk about fiscal stabilizers and money supply rules. We should have a tax rule.

When the economy contracts, there is an automatic stabilizer in that federal government revenue drops. But this is insufficient to fully offset the economic decline. Thus Congress and the President rush to pass or extend tax cuts. But this is a couple of quarters into the recession, and is a very crude response. Further it either expires at some point in the future, or has to be reversed with a politically difficult tax increases.

The auto-stabilizer I propose is to systematically and automatically contract (and increase) tax rates to better absorb the loss and balance the budget in the long run.

Suppose the size of the federal government averages 20% of GDP over time (G = 20%). Over the long term, government spending should equal government revenue. (There is the alternative to inflate  out of debt, but assume this is not an option.)

Imagine we start with a single flat Value Added Tax (VAT) of 20% as the baseline. I use the VAT because it is easy to explain, does not involve marginal rates, and so on. The same idea could be applied to an income tax, or progressive income tax, but it gets complicated, and that is not a virtue.

If GDP contracts by 1% (D = – 1%) , the VAT might contract from 20% to 19% to counteract it. Let’s say spending dropped from \$100 units to \$99 units, keeping the tax rate flat lowers government income by \$0.2 from \$20 units to \$19.8 units, but lowering the rate to 19% contracts government income by 5%, absorbing all of the loss. This stimulates demand by leaving money in the pockets of taxpayers/consumers.

The exact multiplier can be determined, depending on the elasticity of demand to tax rates and so on. If we want to dampen recessions quickly, we cut government revenue 100% in proportion to the change in the size of the economy (i.e., the adjustment factor A = 1). If we want to dampen more slowly (and maintain more government revenue), we can dampen by G*D. So long as D < G, we can dampen up to G. However, the risk is that government revenue goes to zero if we try to absorb all the loss on the government side. If GDP contracts by more than the size of government, the government has to borrow for all operations.  In the extreme, an algorithm might not just reduce taxes to zero, but produce a negative tax. If the VAT were -3%, for instance (due to say a 23% contraction in the economy), everything would be on sale by 3%, a sale paid for by the government by borrowing from the future. This is akin to Friedman’s negative income tax.

When the economy expands, the VAT would increase proportionately until the point that it assured a revenue stream which would pay off the national debt in N years (e.g. N=30). So taxes would rise until they paid for operating costs of government, plus interest on the debt, plus pay down the debt over time. Again the exact amount depends on elasticities etc.

So for instance when GDP rises by 1%, the VAT would increase by between 0% and 1% of GDP. If it increased by 1% it would absorb all the gains, if it increased by 0%, the gains in increased revenue it would be too slow to offset the previous deficit spending. So let’s say the rate increases by the government share of GDP time the change in GDP (G * D). If GDP grew by 1%, and G were 20%, the increase would be 0.2%. If GDP grew at 10%, the rate increase would be 2%. So the government revenue increases both because GDP increases, and because the rate increases by G*D. This increase would continue each quarter until the revenue was projected to be sufficient to pay down the debt in year N, or until the GDP dropped. Thus the increase in taxes would be slower than the reduction.

There would be a quarterly update to the VAT rate based on a formula such as above.

The political economy might be tricky, since we are taking tax rates out of the hands of politicians. On the other hand, responsible politicians who don’t want to vote for tax increases would not have to, since there would be a formula in place which accomplished the main policy objectives of the tax code, raise revenue and act as a counterweight to the economy in general. If government spending rose above the 20%, the tax rate increases phase in to establish a new equilibrium at a higher level, since the rule requires enough revenue to pay off the debt in N years. Budget increases would automatically be captured by a higher tax rate with this rule in place. If the economy expands faster than government spending, the budget would have to eventually be in balance.

Once in place, we would not need active government stimulus spending policies, since that could be done within the tax code. (Nothing prevents Congress from voting for those, but they would add to the long term debt. If a complete stabilizer were used, i.e. government revenue dropped by the entirety of GDP, any spending stimulus would be over-stimulative. If a less than complete stabilizer were used, than spending might be useful.) This does not consider existing federal spending programs like unemployment insurance which have stimulative effect, and might be a justification for using A < 1 in the tax rate adjustments.

Of course, if the economy completely collapses due to unexpected shocks or a breakdown of trust, there isn’t anything the tax code can do to prevent it. But it might reduce the possibility of collapse, and is likely to better handle the run-of-the-mill business cycle (or even a severe shock), which can be dealt with directly, in near real time, through the proposed mechanism.

This would be better with a capital budget, so that N_capital might be 30, but N_operating might be 10. But the gist of the concept is above.

In practice, we may never pay off N, since recessions get in the way, but hopefully by being legitimately on the path to paying off N, there is confidence in the system, that we are on the right path, and government borrowing costs remain low.

The main objection I see is that by decoupling voting for tax increases and voting for spending increases (tax cuts/spending cuts), we make politicians more like drunken sailors than they already are. However, now politicians vote for spending increases without tax revenue and for tax cuts without spending offsets, and this would be a corrective. The new system adjusts tax rates that would automatically, over the long term cover any spending increases. Politicians lose their free lunch. Thus any spending cut brings with it an automatic tax rate cut. Any spending increase an automatic tax rate increase.

I think it might encourage taking things off the consolidated budget, i.e. establishing separate budget streams for different items (social security has a separate funding and spending stream, as do highways (at least “did”, once upon a time)). So long as those independent systems are balanced over time, no problem. We can think of them as separate organizations responsible for specific taxes and specific spending objectives.

We can start the tax rate at the current share of government spending R_{0} = G_{0}. However, if the government is currently in deficit, this might be shock to the system. (For simplicity, I assume government spending has to pay the VAT as well, which may not true, so the rate needs to be adjusted to account for the share of government spending which pays the VAT (buying things) and which does not (redistributing money)).

If for some reason the government holds a surplus (i.e. B< 0), then the government can cut taxes and return that surplus to the people over time.

Along with the quarterly estimate of GDP, there would be a calculation of next quarter’s tax rate. If GDP is up, and the budget is not in balance, tax rates go up, dampening exuberance. If GDP is down, taxes go down, dampening the reaction.

In math:

R_{q} = R_{q-1} + A * D

s.t.

R_{q} ≤ G + B/(Y*N*4)

A = 1 if D < 0,

A = G if D ≥ 0

Where:

R_{q} = tax rate at quarter q (%), applied to all spending, e.g. VAT.

G = government spending share of GDP (Y) (%)

D = quarterly change in GDP (%) (D= (Y_{q} – Y{q-1}) / Y{q-1})

N= number of years to pay off debt

B = sum total of borrowed funds, i.e. debt, in net present value terms

Y = GDP (dollars) quarterly

one can make appropriate assumptions about interest rates, inflation, discounting, I am dealing in Net Present Value Terms here.

I am not a macro-economist, which I am sure is obvious. I have not seen policy discussions of a logic similar to this though. I am also sure there are more sophisticated ways to frame this, which account for the complexities of what is income, on what basis taxes are assessed, and so on. The formulae would not be nearly so elegant after running through the government policy machine. But really, it can’t be worse than existing tax code. My hope is to spur conversation on this.

Also, I am not a lawyer, so I am not sure the constitutionality of this, in that Congress would be adopting a formula for setting tax rates, rather than adopting the rates themselves, but it seems to me it should be okay. And if necessary it could be framed as a set of contingent tax rates spelling out the rates under an enormous number of conditions.

The Congress shall have power to lay and collect taxes on incomes, from whatever source derived, without apportionment among the several States, and without regard to any census or enumeration.