Difference in differences

Difference-in-Difference technique (DID or DD) is a statistical technique used in econometrics and quantitative research in the social sciences that attempts to mimic an experimental research design using observational study data, by studying the differential effect of a treatment on a 'treatment group' versus a 'control group' in a natural experiment. It calculates the effect of a treatment (i.e., an explanatory variable or an independent variable) on an outcome (i.e., a response variable or dependent variable) by comparing the average change over time in the outcome variable for the treatment group, compared to the average change over time for the control group. Although it is intended to mitigate the effects of extraneous factors and selection bias, depending on how the treatment group is chosen, this method may still be subject to certain biases (e.g. mean regression, reverse causality and omitted variable bias).

In contrast to a time-series estimate of the treatment effect on subjects (which analyzes differences over time) or a cross-section estimate of the treatment effect (which measures the difference between treatment and control groups), difference in differences uses panel data to measure the differences, between the treatment and control group, of the changes in the outcome variable that occur over time.

Difference in differences requires data measured from a treatment group and a control group at two or more different time periods, specifically at least one time period before "treatment" and at least one time period after "treatment." In the example pictured, the outcome in the treatment group is represented by the line P and the outcome in the control group is represented by the line S. The outcome (dependent) variable in both groups are measured at time period 1, before either group has received the treatment (i.e., the independent or explanatory variable), represented by the points P₁ and S₁. The treatment group then receives or experiences the treatment and both groups are again measured at time period 2. Not all of the difference between the treatment and control groups at time period 2 (that is, the difference between P₂ and S₂) can be explained as being an effect of the treatment, because the treatment group and control group did not start out at the same point at time period 1. DID therefore calculates the "normal" difference in the outcome variable between the two groups (the difference that would still exist if neither group experienced the treatment), represented by the dotted line Q. (Notice that the slope from P₁ to Q is the same as the slope from S₁ to S₂.) The treatment effect is the difference between the observed outcome and the "normal" outcome (the difference between P₂ and Q).

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