Public Finance — Income and Corporate Taxes: Effects on Work, Saving and Investment

Public Finance — The Income Tax Changes the Price of Work, Saving and Investment

This chapter applies the partial equilibrium analysis of Chapter 2 to the largest taxes. The income tax changes the price of work relative to leisure (the after-tax wage) and the price of future relative to current consumption (the after-tax interest rate). The corporate tax changes the cost of capital for investment and how it is financed. How much each changes behaviour determines the size of the excess burden and of revenue.

1. Labour supply: the direction is settled by data, not theory

A 20% tax on an hourly wage of 10,000 won cuts the after-tax wage to 8,000 won. The change splits into two effects.

Substitution effect: an hour of leisure has become cheaper (less after-tax income is given up), so people take more leisure and work less.
Income effect: the same hours now bring in less income, so people take less leisure and work more (if leisure is a normal good).

Because the two effects work in opposite directions, theory alone cannot say whether a tax increase reduces or raises labour supply. If the income effect grows at high wages, the labour supply curve can even bend backwards.

What determines excess burden, however, is the compensated (Hicksian) elasticity — the substitution effect alone. The income effect is a response to the income taken in tax and would arise just the same under a lump-sum tax. Even if hours do not change at all, a large substitution effect means a large excess burden. The conclusion “people keep working the same after a tax rise, so there is no cost” misreads a case where the two effects cancel.

Summary of empirical labour supply elasticities
Group and response	General conclusion
Hours of primary earners	Small elasticity
Participation of married women and second earners	Relatively large elasticity
Taxable (reported) income of high earners	Respond more by adjusting the timing and form of income than by working

2. The elasticity of taxable income and the revenue-maximizing rate

Modern research looks less at hours than at how taxable income responds to tax rates. Taxable income captures not only work but also changes in the form of compensation, use of deductions and shifting the timing of income. Suppose taxable income has elasticity $e$ with respect to the net-of-tax rate $(1-t)$ .

Taxable income and revenue

z(t) = z_0 (1-t)^{e},\qquad R(t) = t\, z_0 (1-t)^{e}

Raising the rate increases revenue mechanically and reduces it behaviourally as taxable income shrinks. The revenue-maximizing rate, where the two effects are equal, is t* = 1/(1+e).

With $e=0.25$ , $t^*=1/1.25=80\%$ . Above that rate, a rate cut raises revenue. This is the logic of the Laffer curve. The curve itself is not in dispute; the issue is which side of $t^*$ current rates are on, and judging by empirical elasticity estimates (mostly in the range 0.1–0.4), income tax rates in most countries lie to the left of the peak.

The Laffer curve (e = 0.25)

The larger the elasticity, the further left the peak. With e = 1, t* = 50%.

The top rate must also reflect the shape of the distribution of top incomes. The thicker the tail of the income distribution (the smaller the Pareto parameter $a$ ), the more income a rate increase affects. Saez’s formula $t^*=1/(1+a\,e)$ with $a=1.5$ and $e=0.25$ gives about 73%. This is a revenue-maximizing benchmark; the optimal rate is lower depending on how much weight is placed on top earners’ welfare.

3. Taxes on interest and saving

In a two-period model, saving 1 won today allows consumption of $1+r(1-t)$ won tomorrow. With an interest rate of 5% and a 20% tax on interest, the after-tax return is 4%. A tax on interest raises the price of future consumption.

Here too the substitution effect (future consumption is dearer, so save less) and the income effect (more saving is needed to reach a retirement target) work in opposite directions. Empirical estimates of the interest elasticity of saving are small and uncertain. By contrast, the response of the form of saving to tax breaks such as tax-advantaged pension accounts is large. One must always consider that these accounts may merely absorb existing saving without raising total saving.

With inflation, tax on nominal interest raises the effective rate. With a nominal rate of 5%, inflation of 3% and a 20% tax rate, the after-tax nominal return of 4% minus inflation leaves a real return of 1%. Tax takes half of the 2% pre-tax real return, so the effective tax rate in real terms is 50%.

4. The corporate tax: who pays and what it changes

The corporate tax base starts from accounting profit, which differs from economic profit. Interest on debt is deductible as a cost, but the opportunity cost of the equity returned to shareholders is not. The corporate tax therefore favours debt finance. Since excessive debt raises the risk of bankruptcy, some countries have introduced an allowance for corporate equity (ACE) that also deducts the cost of equity.

What affects investment decisions is not the statutory rate but the marginal effective tax rate. Faster depreciation allowances (accelerated depreciation) defer tax and push the effective rate below the statutory rate. Deducting the full cost of investment immediately (full expensing) makes the effective rate on marginal investment zero, leaving tax only on excess profits.

Double taxation: when a corporation pays tax on its profits and distributes the rest as dividends, shareholders pay dividend tax again. With a corporate rate of 20% and a dividend tax of 15%, 100 won of profit leaves $100\times(1-0.2)\times(1-0.15)=68$ won in shareholders’ hands.

Combined tax rate on dividend income

t_{\text{comb}} = t_c + (1-t_c)\,t_d = 0.20 + 0.80\times 0.15 = 0.32

Had the same 100 won been paid as interest, it would have been deducted at the corporate level and subject only to tax on interest income. This difference is another source of debt bias.

A dividend tax credit (gross-up) eases double taxation by returning part of the tax paid at the corporate level to shareholders.

Check your understanding

What is the revenue-maximizing rate when the elasticity of taxable income is 0.5? $t^*=1/(1+0.5)\approx 66.7\%$ . If the current rate rises from 40% to 45%, taxable income becomes $(0.55/0.60)^{0.5}\approx 0.957$ times as large, falling by about 4.3%, but revenue becomes $0.45\times 0.957/0.40\approx 1.077$ times as large, rising by about 7.7%. That is because the economy is to the left of the peak.

References

Jonathan Gruber, Public Finance and Public Policy, ch. 21–24
Emmanuel Saez, Joel Slemrod and Seth Giertz, “The Elasticity of Taxable Income with Respect to Marginal Tax Rates,” Journal of Economic Literature (2012)
Peter Diamond and Emmanuel Saez, “The Case for a Progressive Tax,” Journal of Economic Perspectives (2011)
Harvey Rosen and Ted Gayer, Public Finance, ch. 16–18