How is difference-in-differences estimation useful for economics and finance?

Difference-in-differences (diff-in-diff) is commonly used in scientific and social science experiments to estimate a treatment effect. A treatment group is shocked or treated and the difference in an outcome variable for the treated group is compared with the difference in the same outcome variable for the control group.

In economic studies using observational data, the researcher does not have a clone of a person so that he can shock one and compare the treated person to his un-treated twin. Often times one region - like a state - is shocked while another state is not shocked. A key assumption researchers make when using diff-in-diff estimation with states is that the trend in the outcome variable for the treated state would have been the same as that of the un-treated state had the treated state not be treated. In other words, we do not see the counterfactual world in which the treated state was not treated. We use the untreated state as a proxy for the counterfactual world behavior but the proxy is an assumption.

The diff-in-diff test allows states to differ so long as the differences can be controlled for. States can have a time-invariant state fixed effect. For example, states can have different fixed legal codes that cause constant differences in the outcome variable. The diff-in-diff test also allows the overall environment to change over time - a year effect that is common across states. For example, a bad stock market may influence the outcome variable in all states equally. Controlling for time fixed effects soaks up all of these period-to-period changes common to all states.

The reason the diff-in-diff allows for time-invariant state fixed effects and time fixed effects is because the diff-in-diff ends up subtracting out these fixed effects. The difference from one period to the next of the treatment group knocks out the time-invariant state fixed effect. The difference leaves behind a difference in time fixed effects - i.e. the time fixed effect in period 1 less the time fixed effect in period 0. The next step - the diff-in-diff - then knocks out the common difference in time fixed effects. The remaining quantity is the treatment effect.

One can estimate a diff-in-diff treatment effect using regression. Regress the outcome variable on a constant, dummy for treatment group, dummy for time period and an interaction of the dummy for treatment group and dummy for time period.

A check on the previous diff-in-diff regression is available with panel data. Regress the outcome variable on a state specific intercept a state specific time trend variable, a time fixed effect across states and the treatment dummy, which is 1 if a state is treated in that time period. One can also add other state-specific time trends as regressors too. This approach allows treatment and control states to follow different trends. It is nice if the estimated effect of interest in the previous diff-in-diff regression is unchanged by inclusion of these trends.