Regularization for Nonlinear Panel Models, Estimation of Heterogeneous Taxable Income Elasticities, and Conditional Influence Functions

Individual wants (preferences) and abilities may partly determine prices or tax rates. The resulting simultaneous changes in prices (or taxes) and preferences make it difficult to estimate policy effects of tax or price changes. Panel data, which are repeated observations on individual agents, can help isolate policy effects of price (or tax) changes. If prices change over time while preferences are stable then variation in choices over time can be attributed to price changes. The proposed research will use three projects to develop panel data methods to estimate the effect of price and tax rate changes on economic outcomes and welfare. One project will use big data methods to flexibly model the relationship between preferences and prices while imposing few constraints. The results will be applied to estimate welfare effects of price changes. The second project will estimate a panel data model of taxable income choice given the tax schedule that allows more general heterogeneity than in previous work. This approach will be applied for tax policy evaluation. The third project will develop new methods that can be used to check sensitivity of results from other projects.

With panel data, the distribution of individual preferences given prices (or tax rates) in all time periods is an important, unknown nuisance function that is high dimensional when the number of time periods T is moderate or large. However, time invariance of individual preferences restricts the size of coefficients needed to approximate the nuisance function, suggesting that restricting the size of the coefficients could be useful in practice. The proposed research will use such restrictions to estimate panel data models for moderate to large T. Also, the elasticity of taxable income (ETI) with respect to the net of tax rate is a key parameter for predicting the effect of tax reform and designing income taxes. Recent evidence points to substantial heterogeneity in the ETI across individuals. The proposed research will use panel data to estimate and analyze individual specific ETIs. The proposed research will also develop and analyze conditional influence functions. This work will extend influence function analysis to estimate local sensitivity and construct estimating equations that can be used in debiased machine learning.