The Elasticity of Taxable Income with respect to Marginal Tax

Rates : A Critical Review

E. SaezJ. B. SlemrodS. H. Giertz

NBER 15012, 2009

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Marianne Tenand M1 PPD – 02.11.2010

Why do we want to capture this elasticity?

* Fiscal policy applications :- Deriving the optimal size of the public sector- Quantifying efficiency costs of a form of taxation- Deriving the optimal tax rate(s) [t* = 1/ (1+ε) for PIT]Make an empirical evaluation of the

Equity/Efficiency Trade-Off in income taxation

* Trade-off : results from the impossibility to tax an intrinsic characteristic of individuals

=> Behavorial reactions => deadweight loss for society (a priori) 2

Capturing labor supply elasticity : the quest for the Graal

• Empirical studies and strategies to find ε - The 1st attempts : questionnaires (Fields and Stanbury, 1969, on

lawyers)- Guaranteed Income experiments (USA, Canada) - Taxpayers drain (participation constraint – for richer and poorer taxpayers =>

the elasticity of labor supply of these groups is probably higher than medium-classes’ elasticities)

- Other econometrics studies.• Conclusion : small ec and small η => small ε

=> little efficiency costs of taxing income…?• NOT SO FAST! Troubling evidence that taxpayers react to tax

changes! And in many other ways that just through the number of hours worked.

The revolution of the ETI approach• In reality : income subject to the PIT is not simply equal to

w.L => more relevant concept: reported income, denoted z

- Z includes nbr of hours worked, effort, other forms of income, investment in formation, propensity to report income (evasion), to use tax optimization schemes, etc.

- Takes implicitly account of other, unobservable characteristics of income and tax system

• Model : Max u(c,z) where c = (1-τ)z + E - Gives an individual « reported income » supply function z =

z(1-τ, E) where E is an income not subject to taxation

- No income effect (two channels : E and w). Then :

ETI = (1-τ)/z . dz/d(1-τ)

ETI : empirical strategies• Focus : the upper end of income distribution- Let z+ be the reported income threshold above which taxpayers face a

marginal tax rate of τ- Let zm the average income reported by taxpayers in this top bracket.

zm = zm (1-τ)- The aggregate ETI in the top bracket is

e = (1-τ)/zm . dzm /d(1-τ)= average of individual elasticities weighted by individual income. Then : reported income zi,t = z0

i,t .(1 –τi,t )e individual i, time t.Where z0i,t is the potential income ( reported if τi,t = 0)- Important assumptions : no income effects/ short-term and long-term –responses are

identical/ constant e over time / perfect information

Identifications issues

Log zi,t = e. log (1 - τi,t ) + log z0i,t

* OLS : endogeneity problem since log z0i,t (the unobservable),

is (positively) correlated with τi,t

Solution : find instruments correlated with τi,t but uncorrelated with potential reported income z0

i,t

* Instruments at our reach : changes in tax rates provoked by tax reforms (natural experiments) or unlesgislated changes.

* Where/ when ? USA (mainly) and other developed countries ; exploiting the major tax shifts experienced since the 1970s.

Simple before and after reform comparison

-2SLS with post-reform dummy as instrument for log(1-τi,t )

- comparing z before and after the reform : Δz is attributed to Δ(1-τ)

- Identification condition : log-potential incomes are not correlated with time

-But what about secular growth? business cycles? = Problem of correlation of income with time

- Usually tax reforms affect groups of population in different ways : comparing the changes for these groups?=> other methods possible

= idea of the strategies : comparing changes among different groups

* DD analysis

* Share analysis…

- Identification condition : parallel evolution of the two groups, absent the reform

- Different ways of implementing this strategy

Share analysis

Idea = To control for macro growth, we can normalize incomes of the group affected by a tax change by the average income in the population (if the group is small)

Graph : evolution of the share of top reported income

-Δshare of total income reported by the top percentile

- identification condition : the share of the treatment group changes significantly at the time of the change in his marginal rate while the share of the control group is uncorrelated with the evolution of this marginal rate.

Pt is the share accruing to the top 1% earners in year t.

- Extension : full-time series (using a time-series regression to incorporate more years)

-Concern : e is unbiased if income inequalities would have remained the same (or evoluted randomly) absent the tax reform-=> strong evidence that this hypothesis is violated! (blue arrows)

-The estimate of e is upaward-biased…- finding controls = a challenge…

Upward biasTime-serie identification at risk

Different elasticities for differing groups?

Sensitivity to the specific reform and to the choice of the years Endogeneity

?

Repeated Cross-Section Analysis

Idea : use a tax reform that affected the marginal tax rate of the top 1% (T-group) and that didn’t affect the next 9% (C-group)

Ex : 1993 reform (new brackets with higher rates at the top) (green arrows)

2SLS- Instrument for 1-τi,t : the post-reform and treatment group interaction 1(t=1). 1(i € T)

-Estimate of e = ratio of the pre to post reform change in (log) incomes in the T group minus the same ratio for the C group, to the same DD in the (log) net-of-tax rates

-identification conditions : *the composition of the two groups should not change in a systematic way * the ETI is the same for T and C groups

- estimate is unbiased if the parallel trend assumption holds

-parallel trend assumption is violated (test on pre and post reform)

-Solution : running the 2SLS on several pre- and post-reforms years, adding time trends as controls(implicit hyp : short-term and long-term, transitory and permanent ETI are the same)

- ETI seems to vary accross groups!

Panel Analysis

Idea : use a tax reform that affected the marginal tax rate of the top 1% (T-group) and that didn’t affect the next 9% (C-group.The income groups are defined according to pre-reform (t0) income, and are followed in the post-reform year (t1)

-Estimate of e = very similar to the estimate obtained by cross-section.

-Unbiased if, absent the reform, the (log) income changes are the same for the T and C groups(beware, this assumption mixes together changes in income inequalities and individual income mobility)

- Control for non-tax related change in inequalities

-Mean reversion (transitory incomes)= a big issue => the estimate is very sensitive to the lag between t1 and t0 and the group chosen as control.

- controls for mean-reversion bias and non-tax related change in income distribution = can destroy identification if only 2 years

- to avoid this sensitivity to the base-year income, we can add controls and compare several years (identification : absent the tax change, year-to-year mean reversion and income inequalities change are stable over the period)

Lacks controls (parallel trends violated)

Not sensitive to the choice of the base group

Mean reversion = upward bias with a rate increase (even larger for 49% C-group ; and when lag increases)

Pb of identification

More satisfactory estimates ; even if…

• Conclusions : - share analysis and cross-section analysis seem more robust to

estimate the ETI- But panel analysis may be really performing in specific

circumstances (ex: 1993)

« The most reliable long-run estimates range from 0.12 to 0.4, suggesting that the US marginal top rate is far from the top of the Laffer curve, but greater that one would calculate if the sole behavorial response was labor supply. Estimates for other [developed] countries are, for the most part, in this range. »

The fear - expressed in the 1980s with the Conservative revolution- that in most developed countries marginal tax rates were sub-optimally high, was exaggerated…

- But nonetheless, several issues still need to be tackled…

Further issues (and work for you!)

The studies are still unsatisfactory under certain aspects :- short term vs long term responses - small changes vs large changes in tax rate (question of the perfect

information of taxpayer and of transaction costs)- tax base shifting (application : welfare analysis and change in the

revenue-maximizing tax rate). The authors call for examining closely the “anatomy of response [to tax]”, to distinguish between the many effects incorporated in z.

- Constance of elasticities across time? Across countries?(hypothesis of Kopczuck that e is not a structural parameter, but a function of the income base)

=> In matter of empirical studies on behavioral reaction to taxation, much is still to be done!

References and remarks

More to be found in this article- A bunch of empirical studies (developed countries, other than the USA) are

reviewed in the article- Interesting explanations about fiscal externalities and their consequences on

effective efficiency costs (particularly on tax base shifting : to set optimal tax rates, you must take into account the various existing taxes and their inter-relations)

- In Annexes, details about US databases and tax reforms.

Other texts- Fields, DB and W.T. Standbury. 1971. Income Taxes and Incentives to work : some

additional empirical evidence, AER- Kopczuk, Wojciech. 2005. Tax Bases, Tax Rates and the Elasticity of Reported

Income. Journal of Public Economics- Saez, Emmanuel. 2001. Using Elasticities to Derive Optimal Income Tax Rates.

Review of Economic Studies, 68: 205-229.- Several works of Joel Slemrod, Martin Feldstein, Peter Diamond and James

Mirrless.