Appendix

Appendix A: Implementation Code¶

A.1 Quantile Regression Forest Implementation¶

The following code demonstrates the implementation of Quantile Regression Forests for variable imputation:

from quantile_forest import RandomForestQuantileRegressor

qrf = RandomForestQuantileRegressor(
    n_estimators=100,
    min_samples_leaf=1,
    random_state=0
)

A.2 PyTorch Optimization for Reweighting¶

The reweighting optimization uses PyTorch for gradient-based optimization:

import torch

# Initialize with log of original weights
log_weights = torch.log(original_weights)
log_weights.requires_grad = True

# Adam optimizer
optimizer = torch.optim.Adam([log_weights], lr=0.1)

# Optimization loop
for iteration in range(5000):
    weights = torch.exp(log_weights)
    achieved = weights @ loss_matrix
    relative_errors = (achieved - targets) / targets
    loss = torch.mean(relative_errors ** 2)
    
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

Appendix B: Tables¶

Table A1: Complete List of Imputed Variables¶

Variables Imputed from IRS Public Use File (67 variables)¶

Income Variables:

• employment_income

• partnership_s_corp_income

• social_security

• taxable_pension_income

• tax_exempt_pension_income

• long_term_capital_gains

• short_term_capital_gains

• taxable_ira_distributions

• self_employment_income

• qualified_dividend_income

• non_qualified_dividend_income

• rental_income

• taxable_unemployment_compensation

• taxable_interest_income

• tax_exempt_interest_income

• estate_income

• miscellaneous_income

• farm_income

• alimony_income

• farm_rent_income

• non_sch_d_capital_gains

• long_term_capital_gains_on_collectibles

• unrecaptured_section_1250_gain

• salt_refund_income

Deductions and Adjustments:

• interest_deduction

• unreimbursed_business_employee_expenses

• pre_tax_contributions

• charitable_cash_donations

• self_employed_pension_contribution_ald

• domestic_production_ald

• self_employed_health_insurance_ald

• charitable_non_cash_donations

• alimony_expense

• health_savings_account_ald

• student_loan_interest

• investment_income_elected_form_4952

• early_withdrawal_penalty

• educator_expense

• deductible_mortgage_interest

Tax Credits:

• cdcc_relevant_expenses

• foreign_tax_credit

• american_opportunity_credit

• general_business_credit

• energy_efficient_home_improvement_credit

• amt_foreign_tax_credit

• excess_withheld_payroll_tax

• savers_credit

• prior_year_minimum_tax_credit

• other_credits

Qualified Business Income Variables:

• w2_wages_from_qualified_business

• unadjusted_basis_qualified_property

• business_is_sstb

• qualified_reit_and_ptp_income

• qualified_bdc_income

• farm_operations_income

• estate_income_would_be_qualified

• farm_operations_income_would_be_qualified

• farm_rent_income_would_be_qualified

• partnership_s_corp_income_would_be_qualified

• rental_income_would_be_qualified

• self_employment_income_would_be_qualified

Other Tax Variables:

• traditional_ira_contributions

• qualified_tuition_expenses

• casualty_loss

• unreported_payroll_tax

• recapture_of_investment_credit

Variables Imputed from Survey of Income and Program Participation (1 variable)¶

• tip_income

Variables Imputed from Survey of Consumer Finances (3 variables)¶

• networth

• auto_loan_balance

• auto_loan_interest

Variables Imputed from American Community Survey (2 variables)¶

• rent

• real_estate_taxes