# Background

## 1. Why do we need a staggered DiD package for big data?

Recently, I noticed a pattern at seminars and conferences: presenters would acknowledge that they should use a staggered DiD estimator, but would say that doing so is infeasible in their context due to large sample size. To check, I wrote a simple panel data simulator with staggered treatment roll-out and heterogeneous treatment effects, simulated large samples, and applied these popular R packages for staggered DiD estimation:

- `didimputation` for implementing the approach of Borusyak, Jaravel, and Spiess (2022);
- `did` for implementing the approach of Callaway & Sant’Anna (2021); and
- `DIDmultiplegt` for implementing the approach of de Chaisemartin & D’Haultfoeuille (2020).

I found that only `did` could successfully estimate staggered DiD with 100,000 unique individuals, and it took a while. While many DiD applications consider only a small number of unique individuals (e.g. state-level analysis with 50 states), DiD designs at the household-level or firm-level using administrative data often involve millions of unique individuals.

## 2. This package

I wrote `DiDforBigData` to address 4 issues that arise in the context of large administrative datasets:

1. Speed: In less than 1 minute, `DiDforBigData` will provide estimation and inference for staggered DiD with millions of observations on a personal laptop. It is orders of magnitude faster than other available software if the sample size is large.
2. Memory: Administrative data is often stored on crowded servers with limited memory available for researchers to use. `DiDforBigData` helps by using much less memory than other software.
3. Dependencies: Administrative servers often do not have outside internet access, making it difficult to install dependencies. This package has only two dependencies, `data.table` for big data management and `sandwich` for robust standard error estimation, which are already installed with most R distributions. Optionally, it will use the `fixest` package to speed up the estimation if it is installed. If the `progress` package is installed, it will also provide a progress bar so you know how much longer the estimation will take.
4. Parallelization: Administrative servers often have a large number of available processors, but each processor may be slow, so it is important to parallelize. `DiDforBigData` makes parallelization easy as long as the `parallel` package is installed.

## 3. Demonstration

This section will compare `didimputation`, `did` (using the default option as well as the `bstrap=F` option), `DIDmultiplegt` (with option `brep=40`), and `DiDforBigData` in R. I draw the simulated data 3 times per sample size, and apply each estimator. Results are presented for the median across those 3 draws. Sample Size refers to the number of unique individuals. Since there are 10 simulated years of data, and the sample is balanced across years, the number of observations is 10 times the number of unique individuals. Replication code is available here.

### 3.1 Point estimates

I verify that all of the estimators provide similar point estimates and standard errors. Here, I show the point estimates and 95% confidence intervals (using +/- 1.96*SE) for the DiD estimate at event time +1 (averaging across cohorts). The true ATT is 4 at event time +1. I also verify that two-way fixed-effects OLS estimation would find an effect of about 5.5 at event time +1 when the sample is large.

A caveat: `did` provides standard errors that correspond to multiple-hypothesis testing and will thus tend to be wider than the single-hypothesis standard errors provided by `didimputation` and `DiDforBigData`.

### 3.2 Speed test

Small Samples: Here is the run-time required to complete the DiD estimation using each package:

We see that, with 20,000 unique individuals, `didimpute` and `DIDmultiplegt` have become very slow. I could not get either approach to run successfully with 100,000 unique individuals, as they both crash R. By contrast, `did` and `DiDforBigData` are so fast that they can barely be seen in the plot.

Large samples: Given the failure of `didimpute` and `DIDmultiplegt` with 100,000 observations, we now restrict attention to `did` and `DiDforBigData`. We consider much larger samples:

Even with 1 million unique individuals (and 10 million observations), it is difficult to see `DiDforBigData` in the plot, as estimation requires about half of a minute, versus nearly 1 hour for `did`. Thus, `DiDforBigData` is roughly two orders of magnitude faster than `did` when working with a sample of one million individuals.

### 3.3 Memory test

Small Samples: Here is the memory used to complete the DiD estimation by each package:

We see that `DIDmultiplegt` uses much more memory than the other approaches. The other approaches all use relatively little memory at these sample sizes.

Large Samples:

When considering large samples, we see that `DiDforBigData` uses less than a quarter of the memory used by `did`.