Week 8 (Difference in Difference) Concepts Definition The intuition behind the difference-in-difference approach is that we find two identical groups of people, one of which receives treatment (treatment group) while the other (control group) doesn’t. Hence, since we assumed that these two groups are the same we can attribute the differences to the treatment Example Assuming we have two identical groups of people one of which experiences a policy intervention while the other doesn’t, we have the following: If we instead simply compare the outcome of the treatment group before and after the treatment there may be other factors that may have affected the outcome at the same time of the treatment. Hence to isolate the impact of the treatment we take the differences between post-changes between the two groups. As it allows us to know the average impact of the post-treatment for both groups. Model Estimation Assumptions Parallel Trends ➢ This assumption essentially assumes that if the policy/intervention has not occurred the control and treatment group will have a similar trend over time. Independence ➢ There are no “spillover effects”, which means that the effect of the policy or changes on the treatment group would not have an impact on the control group. If this assumption does not hold the result of the DID estimate is not reliable. Paper Discussion (Feldstein 1995) Abstract Context In this paper, Feldstein wanted to estimate the elasticity of taxable income using a difference-in-difference method through a US tax reform in 1986. The following were the changes: ● Reduced Marginal Income Tax Rates (MTR) for High-Income Individuals ○ Highest MTR fell from 50% to 28% ● Bigger tax base (eg,. capital gains taxed as ordinary income) The aim of the policy is that in spite of the revenue generated will fall this will be offset by the increase within corporate tax income. Data ➢ The data used in this paper is obtained from Form 1040 spanning from 1985 to 1988, which provides individual income tax returns in the US. ➢ There were some data that were excluded from the data set: ○ Taxpayers over the age of 65 in 1988, since retirement, may also cause substantial changes in income. ○ Taxpayers who adopted subchapter S corporation between 1985-1988 ○ Taxpayers with 1985 marginal tax rates below 22%, since a lot of low-income taxpayers post the US treatment at 1986 were no longer in the data. In addition, concerns over mean reversion (individuals who experienced negative income shock may recover back to normal). Benefit and Drawbacks ➢ Panel Data = Since the data is Panel Data we are able to track the individuals in the before and after periods. (Benefit) ➢ Nonstratified Sample = The number of high-income taxpayers is relatively small, hence it reduces the precision of our estimates. (Drawback) ➢ Anomalies in the Sample = Lower income individuals become non-taxable and single individuals who usually marry become the primary taxpayer on the return. ➢ Calculation of Taxable Income = The method by which taxable income was calculated in 1985 was different from how it was calculated in 1988. Empirical strategy Essentially what this paper is trying to achieve is finding the elasticity of taxable income between a pair of marginal tax rate groups. This is done by comparing the differences in the percentage change in taxable income between pairs of marginal tax rate groups to the differences in the percentage change in the net-of-tax rates between the same groups. Issues and Remedy ➢ Changes in Tax Rules ➢ Subchapter C Corporation Basically, since people were utilizing the subchapter C corporation this lowered the individual income tax, hence after the 1986 reform this was no longer allowed, hence this would result in the excluded corporate income appearing at the personal income tax. ➢ Passive Losses ➢ Changes to Personal Exemption Assumption Parallel Trends Justification: Conditions for Parallel Trend to Hold Essentially for parallel trends to hold, we need that the change within the taxable income would be the same across the two periods if the tax reform has not occurred. Elasticity in both groups should be the same for estimates to be consistent. This is a justified assumption as the control group also experiences tax changes, and if the control group were to have changed differently under treatment, then our estimates would be misleading. Evidence Results This method implicitly assumes that there is a relation between the percentage change in taxable income between 1985 and 1988 and the percentage change in the net-of-tax rate with a common "constant term" that does not differ between marginal tax rate groups. The differencing eliminates the common constant term and provides an estimate of the slope term. Since both changes are measured as percentages, this slope coefficient is an estimated elasticity.
