Parameters

Equation 10 of Jacobs et al. [2017] summarizes the equation to determine the social welfare weights. The social welfare weight on a taxpayer with income \(z\) is:

\[ g_z = 1 + \theta_z \varepsilon^c \frac{T'(z)}{(1-T'(z))} + \varepsilon^c \frac{zT''(z)}{(1-T'(z))^2} \]

The parameters/functions that are necessary for computing these social welfare weights are summarized below:

Parameter/Function	Description	Source
\(\varepsilon^c\)	Compensated elasticity of taxable income	Economics literature
\(\theta_z\)	Elasticity of local tax base w.r.t. income \(z\), \(\theta_{z}\equiv 1 + \frac{zf'(z)}{f(z)}\)	See JJZ (2017), will need Tax-Calculator + estimates from economics literature
\(T'(z)\)	Marginal tax rate for each taxpayer	Tax-Calculator
\(T''(z)\)	Derivative of the MTR for each taxpayer	Tax-Calculator (but will need to write a new function)
\(z\)	Pre-tax earnings of each taxpayer	Tax-Calculator/TaxData
\(f(z)\)	pdf of the distribution of earnings	Tax-Calculator/TaxData
\(f'(z)\)	derivative of the pdf of earnings	Tax-Calculator/TaxData

Some notes:

• To start, maybe take a “sufficient statistics” approach

  • Keep elasticities, the income distribution, and employment constant (Jacobs et al. [2017], pg. 86)

  • Otherwise, may need a lot more structure on the model (see Hendren [2014] and Lockwood and Weinzierl [2016]?)

  • Do we need to smooth out MTRs?

    • Maybe just some average effective rate for each point in the income distribution