elas_equalizer: Using elasticity to calculating distance between utility at tangency and at
notch point
Description
Given an elasticity, a budget set, and the earnings of the marginal buncher,
calculate the utility at notch point and at marginal buncher's earning, and
return the absolute difference. Equating these two utilities helps find the
elasticity of the marginal buncher. See equations (3) and (4) at Kelven and
Waseem (2013)
Absolute value of utility at \(zstar+delta_zed\) minus utility at
kink/notch point.
Arguments
elas
elasticity of earnings w.r.t. net-of-tax rate
t1
Tax rate before notch/kink
t2
Tax rate after notch/kink
Tax
Height of notch (zero for pure kink)
zstar
Place of notch/kink (critical earning point)
delta_zed
The notch size in bin units
binw
Bin width
References
Kleven, H. and Waseem, Mazhar (2013) Using notches to
uncover optimization frictions and structural elasticities: Theory and
evidence from Pakistan, The Quarterly Journal of Economics 128(2)
elas_equalizer(0.2, 0.1, 0.2, 100, 1000, 20, 10)
# The elasticity value to minimize this is ~0.0716:elas_equalizer(0.0716, 0.1, 0.2, 100, 1000, 20, 10)