Errors in Variables and Estimated Price Elasticities for Charitable Giving

Researchers often rely on self-reported tax data to gauge the effect of taxes on an economic activity. Such data are subject to measurement errors when individuals intentionally misreport their attributes for tax purposes. To the extent that these intentional reporting errors vary with the tax price and after-tax income, which are important regressors in tax price models, estimated elasticities may be biased. We examine the effect of intentional errors-in-variables in tax price models with an application to charitable giving. We employ a random sample of tax returns subject to extensive audits in order to gauge the magnitude of this potential bias. When the theoretically correct measures of the regressors are used the estimated price elasticity of giving is considerably larger, and the income elasticity is somewhat smaller than conventional estimates using self-reported data. We also find evidence of simultaneity between giving and unreported income. Then, we evaluate the efficacy of using a measure of skewness of the distribution of income (third moment) observed in cross-sectional data as an instrument for the mismeasured variant. We find that this instrument performs reasonably well. Based on this finding, we propose a method to diagnose whether the estimates are subject to measurement error bias and a methodology employing Two-Stage Least Squares to obtain unbiased estimates.