As we saw in Section2, tax to GDP ratios in OECD countries are between 30% and 45% and the more economically meaningful tax to national income ratios between 35%
and 50%. Quantitatively, most estimates of aggregate elasticities of taxable income are
37To see this, if the alternative isτ<τm, everybody below and including the median prefersτmtoτso thatτmwins.
Conversely, ifτ>τm, everybody above and including the median prefersτmtoτandτmstill wins.
38Formula (4) shows that ifzm> Z, then a negative tax rate is actually optimal. Empirically however, it is always the case thatzm< Z.
between .1 and .4 with .25 perhaps being a reasonable estimate (seeSaez, Slemrod, &
Giertz, 2012for a recent survey), although there remains considerable uncertainty about these magnitudes.39
Table2proposes simple illustrative calculations using the optimal linear tax rate for-mula (3). It reports combinations of τ and g¯ in various situations corresponding to different elasticities e (across columns) and different social objectives (across rows). We consider three elasticity scenarios. The first one hase=.25 which is a realistic mid-range estimate (Saez et al., 2012,Chetty, 2012). The second hase=.5, a high range elasticity scenario. We add a third scenario withe = 1, an extreme case well above the current average empirical estimates.
Panel A considers the standard case whereg¯is pinned down by a given social objective criterion andτ is then given by the optimal tax formula. The first row is the Rawlsian criterion (or revenue maximizing tax rate) withg¯ =0. The second row is a utilitarian criterion with coefficient of relative risk aversion (CRRA) equal to one (social marginal welfare weights are proportional to uc = 1/c where c = (1−τ)z+R is disposable income).40Chetty (2006)shows that a CRRA equal to one is consistent with empirical labor supply behavior and hence a reasonable benchmark. The third row is the median voter optimum with a median to average earnings ratio of 70% (corresponding approxi-mately to the current US distribution based on individual adult earnings from the Current Population Survey in 2010). Panel B considers the inverse problem of determining the social preference parameter¯gfor a given tax rate τ. The first row usesτ =35%, corre-sponding to a low tax country such as the United States. The second row usesτ =50%, corresponding to a high tax country such as a typical country from the European Union.
Three points should be noted.
First, panel A shows that an empirically realistic elasticitye =.25 implies a revenue maximizing tax rate of 80% which is considerably higher than any actual average tax rate, even in the countries with the highest tax to GDP ratios, around 50%. The optimal tax rate under the utilitarian criterion with CRRA coefficient equal to one is 61%. The optimal tax rate for the median earner is τ = 55% which corresponds to average tax rates in high tax countries. Correspondingly as shown in panel B, withe=.25, a tax rate of 35%, such as current US tax rates, would be optimal in a situation where ¯g =87%, i.e., with low redistributive tastes. A tax rate of 50% (as in a high tax country) would be optimal with¯g=75%.
Second, a fairly high elasticity estimate ofe=.5 would still generate a revenue maxi-mizing tax rate of 67%, above current rates in any country.The median voter optimum tax
39Note however that the tax base tends to be smaller than national income as some forms of income (or consumption) are excluded from the tax base. Therefore, with existing tax bases, the tax rate needed to raise say 40% of national income, will typically be somewhat higher, perhaps around 50%.
40 ¯gis endogenously determined using the actual US earnings distribution and assuming that government required spendingE(outside transfers) is 10% of total actual earnings. The distribution is for earnings of individuals aged 25 to 64 from the 2011 Current Population Survey for 2010 earnings.
416ThomasPikettyandEmmanuelSaez
Table 2 Optimal Linear Tax Rate Formulaτ=(1−g)/(1−g+e)
Elasticitye=.25 Elasticitye=.5 Elasticitye=1
(empirically realistic) (high) (extreme)
Parameterg(%) Tax rateτ Parameterg(%) Tax rateτ Parameterg(%) Tax rateτ
(1) (2) (3) (4) (5) (6)
A. Optimal linear tax rateτ
Rawlsian revenue maximizing rate 0 80 0 67 0 50
Utilitarian (CRRA=1, uc =1/c) 61 61 54 48 44 36
Median voter optimum(zmedian/zaverage=70%) 70 55 70 38 70 23
B. Revealed preferences g for redistribution
Low tax country (US):Tax rateτ =35% 87 35 73 35 46 35
High tax country (EU):Tax rateτ =50% 75 50 50 50 0 50
Notes:This table illustrates the use of the optimal linear tax rate formulaτ =(1−g)/(1−g+e)derived in the main text. It reports combinations ofτand g in various situations corresponding to different elasticities e (across columns) and different social objectives (across rows). Recall that g is the ratio of average earnings weighted by social marginal welfare weights to unweighted average earnings. Panel A considers the standard case where g is pinned down by a given social objective criterion andτis then given by the optimal tax formula. The first row is the Rawlsian criterion (or revenue maximizing tax rate) withg= 0. The second row is a utilitarian criterion with coefficient of relative risk aversion (CRRA) equal to one (social marginal welfare weights are proportional touc=1/cwherec=(1−τ)z+R is disposable income).gis endogenously determined using the actual US earnings distribution and assuming that government required spending (outside transfers) is 10% of total earnings. The third row is the median voter optimum with a median to average earnings ratio of 70% (corresponding approximately to the current US situation). Panel B considers the inverse problem of determining the social preference parametergfor a given tax rateτ. The first row usesτ=35%, corresponding to a low tax country such as the United States.
The second row usesτ=50%, corresponding to a high tax country such as a typical country from the European Union.
rate of 38% would actually be close to the current US tax rate in that situation. A high tax rate of 50% would be rationalized by¯g=.5,i.e.,fairly strong redistributive tastes.The util-itarian criterion also generates an optimal tax rate close to 50% in that elasticity scenario.
Third, in the unrealistically high elasticity scenario e = 1, the revenue maximizing rate is 50%, about the current tax rate in countries with the highest tax to GDP ratios.
Hence, only in that case would social preferences for redistribution be approaching the polar Rawlsian case.