such that the marginal cost of evasion equals the new tax rate.

Firms choose one of these two responses as a function of their _productivity_ and _fixed cost_ draw (i.e. they select into bunching as a function of their revenue distance to the notch and their costs). For every productivity draw _φi_ in an interval [ _<u>φ,</u> φmax_ ] there exists a fixed cost _αi_ such that all firms within the interval <u>[</u> _<u>φ,</u> φα_ ] bunch at the threshold. _φα_ is determined by the indifference condition between profits at the threshold and profits at the interior solution above the threshold: Π<sup>_Threshold_</sup> ( _y,_ ̃ _y_<sup>_T_</sup> _,_ ̃ _c|φα, α_ )] = Π<sup>_Interior_</sup> ( _y_<sup>_′_</sup> _,_ ̃ _y_<sup>_′_</sup> _,_ ̃ _c_<sup>_′_</sup> _|φα, α_ )], where ( _y,_ ̃ _y_<sup>_T_</sup> _,_ ̃ _c_ ) is the triplet of produced revenue, reported revenue and reported costs at the threshold, and ( _y_<sup>_′_</sup> _,_ ̃ _y_<sup>_′_</sup> _,_ ̃ _c_ ) is the triplet in the interior solution. Firms with _φi > φα_ remain above the threshold and adjust their reporting behavior such that the marginal returns from evasion on revenue and costs equal the higher tax rate.

To illustrate the effect of costs on the bunching decision, consider a firm with productivity _φi >_ _<u>φ</u>_ and fixed cost _αi_ , mapping into produced revenue, reported revenue and costs ( _y_ 0 _,_ ̃ _y_ 0 _,_ ̃ _c_ 0), such that _y_ ̃0 _> y_<sup>_T_</sup> before the tax change. After the tax increase past the threshold, the firm can report revenue at the threshold by reducing revenue with a mix of production and evasion. We denote the production response _dy_ and the evasion response _dy_ ̃. The total change in reported revenue ̃ ̃ is ∆ _y_ = _dy_ + _dy_ , such that ∆ _y_ is the revenue distance to the threshold (∆ _y_ = _y_ 0 _− y_<sup>_T_</sup> ). For small _dτ_<sup>14</sup> the gains from bunching compared to reporting pre-tax change revenue are approximated by: The first term of equation (7) is a noteworthy feature of the Costa Rican corporate income tax: the gains from lowering revenue to reach the threshold are proportional to the change in the tax ̃ rate _dτ_ and to the firm’s reported tax base at the threshold, _y_<sup>_T_</sup> _− c_ 0. Therefore heterogeneity in the fixed cost parameter generates different incentives to bunch for firms of equal productivity. The other terms of equation (7) state that the firm directly gains by not paying taxes on undeclared and unproduced revenue ∆ _y_ , but incurs larger resource costs from the additional revenue underreporting and looses profits due to lower production. Note that if all responses are due to evasion, ̃ ̃ ̃ ̃ then equation (7) simplifies to: _Gains ≈ dτ_ ( _y_<sup>_T_</sup> _− c_ 0) + _dy_ ( _τ_ + _dτ_ ) _− h_<sup>_′_</sup> ( _y_ 0 _− y_ 0 + _dy_ )

# **Prediction 1: Bunching at the revenue thresholds**

The distribution of productivity and fixed cost _f_ ( _φ, α_ ) maps into the distribution of reported revenue and reported costs _ψ_ 0( ̃ _y_ 0 _,_ ̃ _c_ 0) such that a mass of firms bunch at the revenue threshold:

> 14A small _dτ_ allows us to ignore intensive margin responses to the higher tax rate above the threshold. In practice _dτ_ is not small, but we assume so to illustrate the importance of firms’ cost in the bunching decision.

8