# Overview

Difference-in-Difference (DiD) is a powerful technique to evaluate the effects of interventions in observational studies by comparing changes in outcomes between treatment and control groups. But what if interventions aren’t cleanly split between just two groups or two time frames? Enter the world of “staggered” treatments, where **treatments might be rolled out at different times across various units**. Think of promotions introduced in different stores at unique intervals or healthcare policies applied unevenly across regions. In these nuanced situations, the classic DiD might fall short.

Recent studies have highlighted that the conventional approach might be inadequate for staggered treatments and can produce misleading results. Sometimes, these estimates suggest the opposite of what’s happening!

In this topic, we delve into situations where the traditional DiD setup falls short — precisely, those involving staggered treatment timing and many periods. You will gain insights into:

- Understanding staggered treatments in the context of difference-in-difference (DiD) analysis
- The pitfalls of applying classic DiD in these scenarios
- Fundamental assumptions of the staggered DiD method
- Advantages offered by the staggered DiD approach
- Applying staggered DiD using the
`did`

package in R.

## Common Issues with the Conventional DiD Approach

Why is applying the standard DiD setup in staggered treatment scenarios problematic? The traditional DiD framework functions adequately when dealing with scenarios featuring only two periods and a consistent treatment effect. However, in staggered treatment cases, this approach often falls short of capturing the intricacies of real-world dynamics.

Several factors contribute to this limitation, including the potential for the treatment effect to fluctuate over time or among different groups due to learning curves, adaptation, or changing external conditions. Additionally, some units may exhibit immediate responses to treatment, while others might require more time to react. The conventional approach’s one-size-fits-all methodology may need to be revised to account for these variations effectively.

More specifically, the treatment effect estimate in the traditional DiD approach is a weighted average of treatment effects. These weights can sometimes be negative, even if the overall treatment effect is positive. Consequently, this can lead to misleading estimates of the treatment effect, where the average effect appears negative despite the actual positive impact of the intervention. Check out the resources in the **See Also** section at the end of this topic for more details.

## An Illustrative Example: Steps for Staggered DiD Estimation

In this illustrative example, we investigate the impact of the Questions and Answers (Q&A) feature on ratings and reviews within online platforms.

This scenario presents a staggered treatment setup, where various books receive questions at different times. This staggered treatment timing introduces variations that would yield biased estimates when using the conventional DiD framework. To address this issue, we employ a modern DiD technique proposed by Callaway and Sant Anna (2021), implemented using the `did`

package.

This technique offers two primary advantages:

**Enhanced Control Group Selection:**It provides greater flexibility in choosing control groups. Specifically, it allows us to utilize “not-yet treated units” as controls in addition to “never-treated” units. In our context, a book receiving its first question in July 2017 can serve as a control for a book that received its first question in May 2017. The “never-treated” units comprise books on Amazon that never receive questions.**Covariate Incorporation:**This method accommodates the inclusion of covariates, thereby ensuring that the parallel conditions assumption holds conditionally on these covariates.

### Identifying Assumptions

To ensure the validity of staggered DiD estimation, we rely on several key assumptions:

**Staggered treatment adoption:**This assumption posits that once units receive treatment, they remain treated throughout the observation period.**Parallel Trends Assumption with Never-Treated Units:**When we examine groups and periods where treatment isn’t applied $(C=1)$, we assume the average potential outcomes for the group initially treated at time $g$. The group that never received treatment would have followed similar trends in all post-treatment periods $t\geq g$.

Formally, for all $g=2,â€¦, \mathcal{T}, t = 2,…,\mathcal{T} $ such that $t \geq g$, \(\)

$$\mathbb{E}[Y_t(0) - Y_{t-1}|G_g=g] = \mathbb{E}[Y_t(0)-Y_{t-1}(0)|C=1]$$

However, this assumption relies on two important conditions:

(i) There must be a sufficiently large group of units that have never received treatment in our data.

(ii) These never-treated units must be similar enough to the units that eventually receive treatment so that we can validly compare their outcomes.

In situations where these conditions are not met, we can use an alternative parallel trends assumption that involves the **not-yet treated units** as valid comparison groups.

**Parallel Trends Assumption with Not-Yet Treated Units:**When we’re studying groups treated first at time $g$, we assume that we can use the units that are not-yet treated by time $s$ (where $s \geq t$) as valid comparison groups for the group initially treated at time $g$.

Formally, for all $g=2,â€¦,\mathcal{T},s,t=2,…,\mathcal{T}$ such that $t \geq g$ and $s \geq t$,

$$\mathbb{E}[Y_t(0) - Y_{t-1}|G_g=g] = \mathbb{E}[Y_t(0)-Y_{t-1}(0)|D_s = 0, G \neq g]$$

In specific scenarios, considering pre-treatment characteristics (covariates) enhances the credibility of the parallel trends assumption. In such cases, the parallel trends assumptions are conditional, allowing for **covariate-specific trends** in outcomes across groups. This becomes particularly valuable when the distribution of covariates varies among groups.

For instance, various characteristics like popularity, genre, publication date, and more can vary across books when dealing with book-related data. In this context, you would condition the assumption on these relevant book-level characteristics to apply the conditional parallel trends assumption. This means that, before introducing the Q&A feature, books with similar attributes, such as genre, author reputation, or publication date, should have exhibited comparable trends in ratings.

In this example, we use Goodreads as the treatment group and two distinct control groups:

- Control Group 1 (
*Not-yet treated units*): These consist of data from Goodreads only such that books that have not yet received a question by a given period*t*serve as the control group for books that received their first question in period*t*. - Control Group 2 (
*Never-treated units*): Amazon serves as the control group because it enables users to rate and review products but lacks the Q&A feature for books (hence, it is never treated). Note that here, we assume that there are**no time-varying differences**and**spillover effects**(i.e. unintended consequences of potential changes in one platform on the other around the time of the introduction of Q&A).

## Estimation

### Load Data

The dataset consists rating and question data for 5000 unique books on Goodreads and Amazon. The complete set of codes for data processing and estimation can be found in this Gist.

```
# Load packages
library(data.table)
library(dplyr)
library(tidyr)
library(zoo)
library(did)
library(lubridate)
library(googledrive)
library(ggplot2)
#### --- Load data ---###
# Download data from google drive
drive_deauth()
file_id<- "1e-VogI4zQPi_xbSydVLH7PrgkOlWpczl"
drive_download(as_id(file_id), overwrite = TRUE)
GoodAma_sample<- fread("GoodAma_sample.csv")
```

### Data requirements

- The dataset should be in
*long*format where each row corresponds to a particular unit of observation at a particular point in time.

- There must be a unit-specific identifier variable that does not vary over time. In this case,
`asin`

is the book identifier. - There must be a time variable - here it is
`year_month`

. - There must be a group variable, which is usually the period when an individual first becomes treated. For units that are
*never treated*, this variable should be set to 0! In our case,`period_question`

is the group variable that indicates the period a given book receives its first question. - The variables must be of numeric class.

### Effect of Q&A on book ratings

We use the `att_gt()`

function to estimate the group-time average treatment effect. Here, we will estimate using *not yet treated* units as the control group. Still, you can replicate the analysis with the *never treated* units as the control group by setting the control group value to *never treated* or *not yet treated* under the `control_group`

option. Moreover, you may add covariates using the `xformla`

option.

```
staggered_notyettreated <- att_gt(yname = "rating", # outcome variable
tname = "period_review", # time variable
idname = "asin", # id variable
gname = "period_question", # first treatment period variable
control_group = "notyettreated", # set the comparison group as either "never treated" or "not yet treated"
data = goodreads_df, # data
xformla = NULL, # add covariates here but it is set to default in this case
allow_unbalanced_panel = TRUE # indicate whether or not the function should balance with respect to time and id
)
summary(staggered_notyettreated)
```

In cases where there are a large number of groups and time periods, it may be infeasible to interpret all of the group-time average treatment effect coefficients. Thus, we can aggregate group-time average treatment effects using the `aggte()`

function.

```
# aggregate the group-time average treatment effects
staggered_notyettreated_aggregate<- aggte(staggered_notyettreated, type = "dynamic", na.rm = TRUE)
summary(staggered_notyettreated_aggregate)
# Plot group-time ATTs
staggered_notyettreated_plot<- ggdid(staggered_notyettreated_aggregate)+ labs(x = "Time Relative to Q&A Adoption (in 30-day bins)", y = "ATT")
print(staggered_notyettreated_plot)
```

Based on the ATT value, we can conclude that the Q&A feature decreases star ratings by 0.13 stars (p < 0.1).

### Plotting Treatment Effects

Next, we can plot the dynamics of this effect over time using the `ggdid()`

function. All of the data has been reframed in relative event/treatment time.

```
# Plot group-time ATTs
staggered_notyettreated_plot<- ggdid(staggered_notyettreated_aggregate)+ labs(x = "Time Relative to Q&A Adoption (in 30-day bins)", y = "ATT")
print(staggered_notyettreated_plot)
```

Notice how 12 months prior, there are essentially no differences between treatment and control group units which provides some support for the parallel trends assumption. But, post Q&A, the ratings go down.

- Staggered treatment occurs when interventions vary in timing across units or groups.
- Traditional DiD approach works well for cases with two groups and time periods with constant treatment effects but falls short in scenarios with staggered treatments and multiple time periods due to heterogeneous treatment effects and negative weighting issue which can yield misleading estimates.
- Modern DiD techniques offer advantages such as flexible control group selection and the incorporation of covariates.
- Identifying assumptions for staggered DiD include the persistence of treated units and (conditional) parallel trends.
- Staggered DiD can be estimated in R using the
`did`

package. `att_gt()`

is used to estimate group-time average treatment effect.`aggte()`

is used to*aggregate*group-time average treatment effects.`ggdid()`

is used to visualise the treatment effects.

# See Also

- Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey
- Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects
- Estimating dynamic treatment effects in event studies with heterogeneous treatment effects
- The Role of Parallel Trends in Event Study Settings: An Application to Environmental Economics