In Defence of Liberty

Driven by data; ridden with liberty.

The Laffer Curve

In the continuing debate on the 50p rate, Polly Toynbee – The Guardian’s procedural polemicist – argues that: “If it’s not hurting, it’s not working.” Whilst it is fallacious to support a policy by its opposition, Toynbee then makes a strange statement about the Laffer curve:

[London Mayor Boris] Johnson dusts down the old Laffer curve – a long discredited theory convenient for the rich, suggesting lower tax brings in more revenue. But the IMF – no lefties – studying revenue-maximising rates find virtually all countries could raise top rates considerably higher and bring in significant extra sums: the UK and the rest could raise their rates to an optimal 60% or more before they lose more than they gain. The New Pelgrave Dictionary of Economics, reviewing all the research, finds Laffer doesn’t kick in until about 75%.

As Tim Worstall highlights, Toynbee labels the Laffer curve as “discredited”, before pointing out where it applies. The Laffer curve arises out of a mathematical result: Rolle’s Theorem. For a particular tax, tax revenues can be thought of as a smooth function of the tax rate; a function which takes only non-negative values. Thus, there is a revenue-maximising rate, the highest of which necessarily means an increase in tax rates beyond that point causes a decrease in tax revenue. Despite the name, the Laffer curve has clear antecedents in the writings of Ibn Khaldun and John Maynard Keynes. Keynes wrote:

Nor should the argument seem strange that taxation may be so high as to defeat its object, and that, given sufficient time to gather the fruits, a reduction of taxation will run a better chance than an increase of balancing the budget.

TIE Fighters

Unlike its vulgarisation, the Laffer curve does not mean lowering tax rates will automatically inspire greater tax revenues – it simply means that humans respond to tax changes. In the jargon of economists, this responsiveness to income tax changes is called the Taxable Income Elasticity (TIE). This is a number from 0 to 1: the bigger the TIE, the more severe the behavioural response will be.

Differing assumptions on taxable income elasticity have great effects on the projected revenue. (Photo: HM Treasury)

Differing assumptions on taxable income elasticity have great effects on the projected revenue. (Photo: HM Treasury)

HM Treasury surveyed the academic literature, which found TIEs were usually between 0.4 and 0.7. The March 2010 Budget estimates assumed the UK’s TIE was 0.35, since British taxes were supposedly harder to plan against than American taxes, where most papers had studied. The projected income tax revenue is very sensitive to adjustments in the TIE assumption. The HM Treasury report states: “The Laffer curve for the 0.45 TIE shows that he estimated revenue-maximising rate of tax for those with incomes over £150,000 is between 45 per cent and 50 per cent”.

This is why the HM Treasury and the Institute for Fiscal Studies estimates that lowering the additional rate from 50% to 45% reduced income tax revenues by just £0.1bn, though these calculations have large standard errors. Also, this figure does not include any secondary effects on other tax revenues. There is uncertainty over how responsive we are to tax changes, but the Laffer curve itself is not “discredited”.

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4 comments on “The Laffer Curve

  1. Jonathan Bagley
    January 28, 2014

    Thank you for pointing out the Laffer curve is a mathematical truth and just Rolle’s theorem in another guise.

    • Anthony Masters
      January 28, 2014

      Thanks! It’s certainly one of its corollaries.

  2. Tim Worstall (@worstall)
    January 29, 2014

    “The March 2010 Budget estimates assumed the UK’s TIE was 0.35, since British taxes were supposedly harder to plan against than American taxes, where most papers had studied.”

    Hmm. I generally argue that the other way around. UK taxes are easier to avoid than US. For in the UK becoming non-resident is an option. One that’s not available under the US passport based taxation system. You sorta see this being accepted in the Diamond and Saetz paper…..

    • Anthony Masters
      January 29, 2014

      It was a strange assumption, which is why HM Treasury now believes the 50p tax rate raised very little revenue, and may have actually lost tax revenue.

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