5.10 Diff-in-diff analysis

Diff-in-diff is a widely used form of analysis where the effect of a "treatment" is analysed by comparing the change in the average value for a continuous/rankable response variable before/after the time of treatment. This is done for two groups:

• Treatment group

• Control group

Finally, the difference between the two groups is calculated.

The following preparatory steps must be followed before running a diff-in-diff analysis:

1. Create a panel dataset through the command import-panel or by converting from "wide" format to "long" format through the command reshape-to-panel.

2. Create a group variable with the value 1 for the treatment group and 0 for the control group.

3. Create a treatment variable that is set to 0 for all times before the treatment time, and 1 for all times starting from the treatment time.

After following steps 1. - 3. the command regress-panel-diff is used.

The dependent variable is listed first. It must be continuous or rankable. The group and treatment variables need to be listed as numbers 2 and 3. This is a prerequisite for the analysis to be carried out correctly. Other independent variables are listed at the end (optional).

The result from regress-panel-diff shows a standard panel regression table with model measures and coefficient values. The diff-in-diff value (so-called ATET value - average treatment effect of the treated) corresponds to the coefficient value of the interaction term for the two dummy variables which indicate respectively group and treatment.

Example:

Random selection with panel extraction for the years 2018-2021. Uses women as the treatment group and men as the control group. The treatment time is set to 2020. Diff-in-diff value (ATET) is equal to -1991.77 when controlling for marital status = married, place of residence = Oslo, and educational level equal to a master's degree or higher. The ATET value is not significant in this case.

The command regress-panel-diff is equivalent to running regress-panel with the option pooled where the group and treatment variables are included as interaction terms as well as separate dummies (use the characters ## to express this).

Example:

 regress-panel-diff salary group treatment married oslo high_edu

gives the same result as

 regress-panel salary group##treatment married oslo high_edu, pooled

The following options are available for regress-panel-diff:

• level(): Define a significance level other than the default value of 95 (5% significance level)

• robust: Robust standard deviations

• cluster(): Cluster estimation

The command help regress-panel-diff generates more information about the available options.

IMPORTANT

Time (e.g. factor terms such as i.year) should not be included in regression-panel-diff models, as you risk obtaining 100% equal variance for the treatment variable compared with the dummy terms linked to the years from and including the time of treatment. The coefficient estimates for the variables/terms involved will then be incorrect as a result.

 $\rhd$ Example on data adaptation for diff-in-diff analysis

NB!

If you create a panel dataset using import-panel, measurement dates are processed with the UnixTime format, and you must then use the function year() to extract /refer to the year, as in the example above:

 replace treatment = 1 if year(date@panel) >= 2020

If you instead use reshape-to-panel to create a panel dataset, you are the one who controls the value format for the measurement dates through the use of suffixes on the variables (usually two-digit or four-digit years), and you must then take care to adapt the replace expression so that it matches the format of date@panel. If you use a suffix that indicates a four-digit year (YYYY), this will also be the format of the values ​​for date@panel. Then you should not use year() since this is only intended for use with UnixTime formats. In this case, you must refer to the year as follows:

 replace treatment = 1 if date@panel >= 2020