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Working paper

Regression Estimates of the Elasticity of Taxable Income and the Choice of Instrument (WP 13/08)

Issue date: 
Monday, 8 April 2013
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Publication category: 
JEL classification: 
H24 - Personal Income and Other Nonbusiness Taxes and Subsidies; includes inheritance and gift taxes
H31 - Fiscal Policies and Behavior of Economic Agents: Household

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This paper examines estimation of the elasticity of taxable income using instrumental variable regression methods.


This paper examines estimation of the elasticity of taxable income using instrumental variable regression methods. It is argued that the standard instrument for the net-of-tax rate - the rate that would be applicable post-reform but with unchanged income levels - is unsatisfactory in contexts where there are substantial exogenous changes in taxable income. Two alternative tax rate instruments are proposed, using estimates of the dynamics of taxable income for a panel of taxpayers over a period that involves no tax changes. The parameters derived from this procedure are then used to construct counterfactual post-reform incomes that would be expected in the absence of reform. The first method is based on the tax rate each individual would face if income were equal to expected income, conditional on income in two periods before the tax change. The second alternative uses the form of the conditional distribution of income for each taxpayer to obtain an instrument based on the expected tax rate. The methods are applied to the tax change in New Zealand in 2001. It is found that the proposed new instruments significantly outperform the standard instrument, in particular there are substantial improvements using the expected tax rate.

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We are grateful to the Royal Society of New Zealand for funding support from the Cross Departmental Research Pool from Government. The views expressed in this paper are our own and not necessarily those of Inland Revenue or Treasury. We benefited at an early stage from discussions with Raj Chetty. We are also grateful for comments on earlier versions from Jared Bullen, Nick Carroll, Richard Disney, David Law, Jose Sanz-Sanz, Sandra Watson and participants at the New Zealand Association of Economists 2012 Conference.


The views, opinions, findings, and conclusions or recommendations expressed in this Working Paper are strictly those of the author(s). They do not necessarily reflect the views of the New Zealand Treasury or the New Zealand Government. The New Zealand Treasury and the New Zealand Government take no responsibility for any errors or omissions in, or for the correctness of, the information contained in these working papers. The paper is presented not as policy, but with a view to inform and stimulate wider debate.

Last updated: 
Wednesday, 10 April 2013