bunching evidence from Hungary

MAGYAR NEMZETI BANK
Figure 2
Minimum revenue tax schedule when the sum of tax base modifying items () < 0
Tax amount
0 .01 .02 .03 .04 .05 .06 .07
2% Y τ
Δ τ
(Y - C) τ
(Y - C + Δ) τ
0 .02 .04 .06
[ Y - C ] / Y = 2%
Profit ratio
rates. Aer the introducon of the minimum tax scheme a kink point is introduced in the tax liability schedule. With the new
tax regime firms to le of the cutoff face an incenve to reopmase their reporng and to increase their reported profit rate
ll the cutoff either via reducing over-reporng cost items or producon, while firms above the cutoff are not affected. Firms
in some interval [ ∗ ∗ , ∗ ] – where ∗ is the 2 percent cutoff – will find it more profitable to increase their reported profit
ll the cutoff and create an excess mass in the distribuon. The marginal buncher firm is originally located at the ∗ ∗
profit rate, and all firms originally located between the marginal buncher and the 2 percent cutoff move to the kink point.
Firms located below the marginal buncher will also increase their reported profit rate aer the reform and fill up the hole in the
interval [ ∗ ∗ , ∗ ]. Assuming two hypothecal populaons of firms facing the same tax reform, the further the marginal
buncher is from the cutoff, the larger the firms’ response to the reform. How far from the le of the cutoff the marginal buncher
is coming from can be linked to the amount of excess bunching based on the formula:
∗
B h 0 ()d ≃ h 0
̄ () ∗ , (7)
∗ ∗
where B is total bunching mass that is esmated based on the empirical distribuon, and h 0 () is the counterfactual density
on the interval [ ∗ ∗ , ∗ ]. The marginal buncher (b) can be backed out b B/ h 0
̄ ().
The counterfactual distribuon (i.e. the distribuon that would have been without the kink or the notch) is esmated by fing
a polynomial on the actual empirical distribuon where the bunching interval is excluded, then predicted fied values are
calculated for the excluded range. Finally, the excess mass is the difference between the actual and counterfactual distribuon.
A drawback of this counterfactual esmaon strategy is that it does not take into consideraon extensive margin responses. To
overcome this laer problem a novel characterisc of my esmaon strategy is that I compare the empirical distribuon directly
to the actual pre-reform distribuon, and not to a hypothecal counterfactual. I calculate bootstrapped standard errors for the
point esmate of b by taking samples (with replacement) of the distribuon a large number of mes (N=1000), esmang the
point esmates corresponding to these bootstrap samples, and then calculang the sample standard deviaon of the sampling
distribuon of b .
The methodology is similar in case of the tax schedule with a notch point. The marginal bunching firm is originally located at
the ∗
profit rate, where ∗ is the 2 percent cutoff, and all firms between the marginal buncher and the cutoff move
to the notch point. In case of the notched tax schedule firms face an addional incenve to bunch above the cutoff. The
10 MNB WORKING PAPERS 3 • 2016